1. Hopf Topology Archive, Revised Version Seminars at Purdue. algebraic topology Discussion Group Archives maintained by DonDavis. HTTP uploading of submissions. Newer Photographs on Hopf. Time capsule http://hopf.math.purdue.edu/pub/hopf.html

Hopf Topology Archive Welcome to the Hopf Topology Archive! Hopf Author/Title Search: enter author or title keyword into box below. PaperSearch The Hopf Logos The Hopf Archive, month by month listing. CDROM of current Hopf Archive (April 4, 2002) (650MB ) This archive list is current through October 2002. Newer files may be in the proper directories but not listed on the html list. These are accessible as http://hopf.math.purdue/AuthorName <- usually last names of authors. If you have a submission that has not been announced or posted and some time has elapsed, please email Mark and Clarence (but please try the "Reload" button on your browser first. Thanks, Clarence) Hopf has been upgraded to faster CPU and disk. Hope it helps the service. Also, HTTP uploading (http://hopf.math.purdue.edu/upload.php) has been added. Clarence What's New! Uploading Preprints Latest maintained by Mark Hovey. Back issues of Mark's What's New! Seminars at Purdue Algebraic Topology Discussion Group Archives maintained by Don Davis HTTP uploading of submissions.

2. Algebraic Topology Discussion List The primary functions of this list are providing abstracts of papers posted to the Hopf archive, Category Science Math Topology......algebraic topology Discussion List. This topology. This website also servesas an archive of links to websites related to algebraic topology. http://www.lehigh.edu/~dmd1/algtop.html

Algebraic Topology Discussion List This list is maintained by Don Davis. To subscribe or unsubscribe or post a message for the list, send e-mail to dmd1@lehigh.edu. The primary functions of this list are the first three items listed below: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology. This website also serves as an archive of links to websites related to algebraic topology. The Hopf archive is a preprint server for papers in algebraic topology. It is maintained by Clarence Wilkerson. Every few weeks, Mark Hovey posts abstracts of papers which have been added to the Hopf archive. Information about conferences Other posted messages List of e-mail addresses of people on the list . There are more than 500 subscribers. Links to home pages of algebraic topologists Links to other sites related to algebraic topology (books, journals, tables, research groups, ongoing seminars, other sites) As a new service for the nonspecialist, we have an

3. Essays About Algebraic Topology Essays about algebraic topology. What is topology?, by Bob Bruner (Wayne StateUniv); What is algebraic topology?, by Joe Neisendorfer (Univ of Rochester); http://www.lehigh.edu/~dmd1/essays.html

Essays about algebraic topology Survey articles for the general public Topology articles from Eric Weisstein's World of Mathematics , sponsored by wolfram.com. Geometry/topology section of Mathematical Atlas , coordinated by Dave Rusin (Northern Illinois Univ) What is topology? , by Bob Bruner (Wayne State Univ) What is algebraic topology? , by Joe Neisendorfer (Univ of Rochester) What is topology? , by Neil Strickland (Univ of Sheffield) Encyclopedia article about topology , by Don Davis (Lehigh Univ) Survey articles about topics in topology, written for nonspecialists with some knowledge of mathematics Higher dimensional group theory , by Ronald Brown (Univ of Wales, Bangor) Knot Theory , by knot group at Univ of Wales, Bangor

4. AMS Online Books/COLL27 by Solomon Lefschetz Publication Date 1942 Number of Pages 389 pp. Download Individual Chapters FREE (10 files - 41.5mb) Bibliography and Indexes Title List Help AMS Home AMS Bookstore. algebraic topology. by Solomon Lefschetz http://www.ams.org/online_bks/coll27

Title List Help AMS Home AMS Bookstore Algebraic Topology by Solomon Lefschetz Publication Date: 1942 Number of Pages: 389 pp. Publisher: AMS ISBN: 0-8218-3397-9 COLL/27.E Download Individual Chapters FREE (10 files - 41.5mb) Frontmatter Title Contents Preface Introduction to General Topology Additive Groups Complexes Complexes: Products. Transformations. Subdivisions ... Endmatter Appendices Bibliography and Indexes Comments: webmaster@ams.org Privacy Statement

5. Nantes 3-7 Sept 2001 space homology, Cyclic Homology, Algebraic Ktheory. algebraic topology coming from problems of Geometric Topology, e.g. http://www.math.sciences.univ-nantes.fr/~franjou/2001.html

http://www.math.sciences.univ-nantes.fr/~franjou/2001.html En francais last modified: July 19, 2001 UMR 6629 G.D.R.E.1110 Algebraic Topology Conference University of Nantes September 3 - 7 , 2001 Deadline for registration: July 6, 2001. Registration is now closed Check your registration: please check that your name appears in the List of registered participants . If you do not appear on the list, although you sent us registration, please re-send the form at NCAT@math.univ-nantes.fr Get updated information http://www.math.sciences.univ-nantes.fr/~franjou/2001pratique.html Scientific program Schedule of talks List of registered participants ... Maps SCIENTIFIC PROGRAM The scientific program concerns main research fields in Modern Homotopy Theory: Algebraic Homotopy Theory, Unstable Modules over the Steenrod algebra, MacLane Homology, Operads, Loop space homology, Cyclic Homology, Algebraic K-theory. Algebraic Topology coming from problems of Geometric Topology, e.g. Knot Theory, Low dimensional Manifolds, Foliations, will also be included. The Program will contain one hour keynote talks by invited speakers, three lectures on Knot Invariants

6. 55: Algebraic Topology 55 algebraic topology algebraic topology is the study of algebraic objects attached to topological spaces; the algebraic invariants reflect some of the topological structure of the spaces. http://www.math.niu.edu/~rusin/known-math/index/55-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 55: Algebraic topology Introduction Algebraic topology is the study of algebraic objects attached to topological spaces; the algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fiber bundles and related spaces are included here, while complexes (CW-, simplicial-, ...) are treated in section 57. Finally, the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences; the machinery (mostly derived from homological algebra) is powerful if rather daunting. In all cases, the "naturality" of the construction implies that a map between spaces induces a map between the groups. Thus one can show that no maps of some sort can exist between two spaces (e.g. homeomorphisms) since no corresponding group homomorphisms can exists. That is, the groups and homomorphisms offer an algebraic "obstruction" to the existence of maps. Classic applications include the nonexistence of retractions of disks to their boundary and, as a consequence, the Brouwer Fixed-Point Theorem. (Obstruction theory is, more generally, the creation of algebraic invariants whose vanishing is necessary for the existence of certain topological maps. For example a function defined on a subspace Y of a space X defines an element of a homology group; that element is zero iff the function may be extended to all of X.)

7. Allen Hatcher's Homepage Contains textbooks in algebraic topology, KTheory, and 3-Manifolds.Category Science Math Topology algebraic topology...... http://www.math.cornell.edu/~hatcher/

Allen Hatcher Office: 553 Malott Hall Phone: (607)-255-4091 E-mail . The address is hatcher@math.cornell.edu Cornell Math Dept Homepage Cornell Topology Festival Nature Photos On This Webpage: Book Projects: Algebraic Topology Vector Bundles and K-Theory Spectral Sequences in Algebraic Topology ... Papers Book Projects Real and Imaginary Algebraic Topology In an excess of youthful enthusiasm in the late 1980's I started writing an algebraic topology book with the ambitious goal of covering all the basics while yet remaining readable by newcomers seeing the subject for the first time. As the magnitude of the task gradually became apparent, the end of the book receded farther and farther into the distance. Eventually the book split into two volumes, then three. The first volume, which is now finished, contains the basic core material along with a number of optional topics of a relatively elementary nature. The other two volumes, which are largely independent of each other, are provisionally titled "Vector Bundles and K-Theory" and "Spectral Sequences in Algebraic Topology." These are only partially written see below. To find out more about the first book or to download it in electronic form, follow this link to the download page Vector Bundles and K-Theory The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. For further information, and to download the part of the book that is written, go to

8. Algebraic Topology Book In Dave Rusin's Mathematical Atlas.Category Science Math Topology algebraic topology...... the algebraic invariants reflect some of the topological structure of the http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Algebraic Topology To get an idea of what's in the book you can look at the Table of Contents and the Preface Printed Version . The book has been published by Cambridge University Press in a paperback edition (ISBN 0-521-79540-0) for US$30 and a hardback edition (ISBN 0-521-79160-X) at a considerably higher price. It is now in a third printing, with corrections of some minor errors in the earlier printings. (See farther down this page for a list of the corrections.) Electronic Version: By special arrangement with the publisher, an online version will continue to be available for download here. Individuals may print out single copies for their own use, but xeroxing multiple copies is not allowed. There are several different formats available. First of all, you can download the whole book as a single rather large pdf file (3.5Meg) of about 550 pages. If you wish to save paper when you print it out, there is also a pdf doublepage version with two pages side by side, reduced in size so that they fit on one sheet of standard US size paper, and probably also on European size paper. Another option is to download the individual chapters separately. These are available in both pdf and postscript formats. The postscript files are compressed as zip files, but they are still quite a bit larger than the pdf files. To get enough material for a one-semester introductory course you could start by downloading just Chapters 0, 1, and 2, along with the Table of Contents, Bibliography and Index. Here are the individual parts:

9. Dynamic Directory - Science - Math - Topology - Algebraic Topology Hatcher's Homepage Contains textbooks in algebraic topology, K-Theory, and 3-Manifolds. Algebraic K-theory, Groups http://www.maximumedge.com/cgi/dir/index.cgi/Science/Math/Topology/Algebraic_Top

var AdLoaded = false; var bsid = '18707'; var bsads = '6'; var bsloc = ''; var bswx = 468; var bshx = 60; var bsw = '_top'; var bsb = 'FFFFFF'; var bsf = '000000'; var bsalt = 'off'; MaximumEdge.com Search E-Mail News ... Maps Dynamic Directory Top Science Math Topology :Algebraic Topology Categories Web Pages See also: Science: Math: Algebra: Category Theory Allen Hatcher's Homepage - Contains textbooks in Algebraic Topology, K-Theory, and 3-Manifolds. Algebraic K-theory, Groups and Categories - Report of a research programme at the University of Wales, Bangor. Algebraic K-Theory, Linear Algebraic Groups and Related Structures - TMR network coordinated in Bielefeld. Algebraic Topology - In Dave Rusin's Mathematical Atlas. Algebraic Topology and Concurrency - Applications of algebraic topology to computer science. Algebraic Topology by Solomon Lefschetz - Published by the AMS, available for free download as PDF files. Algebraic Topology Discussion List - Information on subscribing, archives of past discussions, and links to home pages of algebraic topologists. Ext Charts - Ext charts for modules over the odd-primary Steenrod algebra by Christian Nassau.

10. Handbook Of Algebraic Topology Publisher's page. Contents, ordering information.Category Science Math Topology algebraic topology...... http://www.elsevier.nl/locate/hat

Home Search What's New Electronic Services ... Links Handbook of Algebraic Topology Book Information Description Contents Bibliographic and Ordering Information Contents Services Extended Contents Foreword List of Contributors Subject Index ... Related Info NORTH-HOLLAND Last update: 15 Mar 2003

11. The Math Forum - Math Library - Algebraic Topology The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to algebraic topology. Selected Sites (see also All Sites in this category). algebraic topology Dave Rusin; The Mathematical Atlas http://mathforum.com/library/topics/alg_topol

Browse and Search the Library Home Math Topics Topology : Algebraic Topology Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Algebraic Topology - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fibre bundles and related spaces are included here... the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> AT Algebraic Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis

12. Algebraic Topology & Concurrency Applications of algebraic topology to computer science.Category Science Math Topology algebraic topology......No frames. http://www.ipipan.gda.pl/~stefan/AlgTop/

No frames No frames

13. Reports Directory of reports applying methods in algebraic topology to concurrent computation, following the Category Computers Computer Science Asynchronous Computability...... algebraic topology and Concurrency. To appear in Theoretical Computer Science. Algebraictopology in scheduling problems. Preprint R96-2013, Dept. http://www.ipipan.gda.pl/~stefan/AlgTop/reports.html

Reports For more up to date versions and for more complete listing of reports see the authors' home pages S. Blanc, Rachid Guerraoui , K. Hess, Petr Kouznetsov , P. E. Parent, Bastian Pochon , O. Sauvageot. Using the Topological Characterization of Synchronous Models. Preliminary Proceedings of GETCO 2002, Toulouse, France, BRICS Notes NS-02-5 , 13 pages. October 2002. Ulrich Fahrenberg Ditopology. Part 2 (pages 45-63) in Geometry and Topology by Ulrich Fahrenberg and John-Josef Leth. Student Project, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark. Ulrich Fahrenberg Towards an Efficient Algorithm for Detecting Unsafe States in Timed Concurrent Systems. M.Sc. thesis, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark. Lisbeth Fajstrup Dicovering spaces. Report R-01-2023, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark. November 2001. Lisbeth Fajstrup , Eric Goubault , Martin Raussen Algebraic Topology and Concurrency. To appear in Theoretical Computer Science . Also preprint R-99-2008, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark.

14. Index The emphasis of the conference is on categorical decomposition techniques, especially calculus of Category Science Math Topology Events Past Events......International Conference in algebraic topology Isle of Skye Scotland 24-30 June 2001 Research Centre in Topology and Related Areas Department of http://www.maths.abdn.ac.uk/~stc2001/

International Conference in Algebraic Topology Isle of Skye - Scotland 24- 30 June 2001 Research Centre in Topology and Related Areas Department of Mathematical Sciences University of Aberdeen An international Algebraic Topology conference is planned for the last week of June 2001 (June 24 - 30, 2001). The conference will take place on the Isle of Skye - a scenic island off the west coast of Scotland. The emphasis of the conference is on categorical decomposition techniques, especially calculus of functors and homology decompositions of classifying spaces. But the conference is intended to have a broad scope, with talks on a variety of topics of current interest in topology. A London Mathematical Society invited lecture series will take place in Aberdeen the week before the conference (June 18 - 23, 2001). Prof. T. Goodwillie will give a series of ten lectures on calculus of functors. Participants who wish to attend both meetings are encouraged to do so and will enjoy reduced registration fees. The following mathematicians have agreed to attend and give a plenary talk.

15. Algebraic Topology -- From MathWorld algebraic topology, The discipline of algebraic topology is popularly known as rubbersheetgeometry and can also be viewed as the study of disconnectivities. http://mathworld.wolfram.com/AlgebraicTopology.html

Topology Algebraic Topology Algebraic Topology The study of intrinsic qualitative aspects of spatial objects (e.g., surfaces spheres tori circles ... links , configuration spaces, etc.) that remain invariant under both-directions continuous one-to-one homeomorphic ) transformations. The discipline of algebraic topology is popularly known as " rubber-sheet geometry " and can also be viewed as the study of disconnectivities . Algebraic topology has a great deal of mathematical machinery for studying different kinds of hole structures, and it gets the prefix "algebraic" since many hole structures are represented best by algebraic objects like groups and rings A technical way of saying this is that algebraic topology is concerned with functors from the topological category of groups and homomorphisms . Here, the functors are a kind of filter, and given an "input" space , they spit out something else in return. The returned object (usually a group or ring ) is then a representation of the hole structure of the space , in the sense that this algebraic object is a vestige of what the original space was like (i.e., much information is lost, but some sort of "shadow" of the

16. Algebraic Topology - Wikipedia algebraic topology. algebraic topology is a branch of mathematics in whichtools from abstract algebra are used to study topological spaces. http://www.wikipedia.org/wiki/Algebraic_topology

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Algebraic topology From Wikipedia, the free encyclopedia. Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces The goal is to take topological spaces, and further categorize them by mapping them to groups , which have a great deal of structure. Two major ways in which this can be done are through fundamental groups , or homotopy, and through homology /cohomology groups. Fundamental groups give us crucial information about the structure of a topological space, but they are often nonabelian and can be difficult to work with. Homology/Cohomology groups, on the other hand, are abelian, and in many important cases even finitely generated. Finitely generated abelian groups can be completely classified and are particularly easy to work with.

17. Stable Algebraic Topology 1945-1966, By J.P. May Stable algebraic topology 19451966, by JP May. This is a reasonablycomprehensive treatment of the history of stable algebraic topology http://www.math.uiuc.edu/K-theory/0321/

Stable algebraic topology 1945-1966, by J.P. May This is a reasonably comprehensive treatment of the history of stable algebraic topology during the cited period. The table of contents gives an idea of the scope and limitations of the study. The emphasis is on the evolution of ideas, but some mathematical exposition of most of the main results is given. This paper will appear in a volume on the history of topology that is being edited by Ioan James. Contents: Setting up the foundations The Eilenberg-Steenrod axioms Stable and unstable homotopy groups Spectral sequences and calculations in homology and homotopy The introduction of cobordism The route from cobordism towards K-theory Bott periodicity and K-theory The Adams spectral sequence and Hopf invariant one S-duality and the introduction of spectra Oriented cobordism and complex cobordism K-theory, cohomology, and characteristic classes Generalized homology and cohomology theories Vector fields on spheres and J(X) Further applications and refinements of K-theory Bordism and cobordism theories Further work on cobordism and its relation to K-theory High dimensional geometric topology Iterated loop space theory Algebraic K-theory and homotopical algebra The stable homotopy category The Bibliography lists over 300 items.

18. The Math Forum - Math Library - Algebraic Topology This page contains sites relating to algebraic topology. Browse and Searchthe Library Home Math Topics Topology algebraic topology. http://mathforum.org/library/topics/alg_topol/

Browse and Search the Library Home Math Topics Topology : Algebraic Topology Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Algebraic Topology - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fibre bundles and related spaces are included here... the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> AT Algebraic Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis

19. About "Algebraic Topology" algebraic topology. Library Home Full Table of Contents Suggest a Link Library Help Resource Types Articles. Math Topics algebraic topology. http://mathforum.org/library/view/4261.html

Algebraic Topology Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.math.niu.edu/~rusin/known-math/index/55-XX.html Author: Dave Rusin; The Mathematical Atlas Description: A short article designed to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fibre bundles and related spaces are included here... the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. Levels: College Languages: English Resource Types: Articles Math Topics: Algebraic Topology Suggestion Box Home The Math Library ... Search http://mathforum.org/

20. Algebraic Topology Authors/titles Recent Submissions algebraic topology. Keywords and phrases Intersection Cohomology, StratifiedPseudomanifolds Subjclass algebraic topology MSC-class 35S35; 55N33 http://arxiv.org/list/math.AT/recent

Algebraic Topology Authors and titles for recent submissions Tue, 18 Mar 2003 Mon, 17 Mar 2003 Fri, 14 Mar 2003 Thu, 13 Mar 2003 ... Tue, 11 Mar 2003 Tue, 18 Mar 2003 math.AT/0303207 abs ps pdf other Title: Combinatorial classes on the moduli space of curves are tautological Authors: Gabriele Mondello Comments: 25 pages, 2 figures (xypic), LaTeX2e Subj-class: Algebraic Topology; Algebraic Geometry MSC-class: Mon, 17 Mar 2003 math.AT/0303177 abs ps pdf other Title: Changement de base pour les foncteurs Tor Authors: Mathieu Zimmermann Comments: 11 pages Subj-class: Algebraic Topology MSC-class: math-ph/0303035 abs ps pdf other Title: Discrete connections on the triangulated manifolds and difference linear equations Authors: S.P.Novikov Comments: 25 pages, Latex Subj-class: Mathematical Physics; Differential Geometry; Algebraic Topology Fri, 14 Mar 2003 math.AT/0303164 abs ps pdf other Title: Stanley-Reisner rings and torus actions Authors: Taras E. Panov (Moscow State University and ITEP) Comments: 28 pages, LaTeX2e Subj-class: Algebraic Topology; Commutative Algebra; Combinatorics MSC-class: math.AT/0303157

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