Geometry.Net - Pure_And_Applied_Math: Algebraic Topology

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

Extractions: PaperSearch The Hopf Logos 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 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.
Algebraic Topology Discussion List
The primary functions of this list are providing abstracts of papers posted to the Hopf archive, Category Science Math Topologyalgebraic 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

Extractions: 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. As a new service for the nonspecialist, we have an
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
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
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

Extractions: 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 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.
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

Extractions: POINTERS: Texts Software Web links Selected topics here 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.)
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/

Extractions: On This Webpage: Book Projects: Papers Book Projects Real and Imaginary 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 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
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

Extractions: 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:
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

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

Extractions: 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
Algebraic Topology & Concurrency
Applications of algebraic topology to computer science.Category Science Math Topology algebraic topologyNo frames.
http://www.ipipan.gda.pl/~stefan/AlgTop/
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
Index
The emphasis of the conference is on categorical decomposition techniques, especially calculus of Category Science Math Topology Events Past EventsInternational 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/

Extractions: 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.
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

Extractions: 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
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

Extractions: 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 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.
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/

Extractions: 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.
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/

Extractions: 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
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

Extractions: 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
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

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