41. Papers By AMS Subject Classification No papers on this subject. 55XX algebraic topology / Classification root.55-00 General reference works (handbooks, dictionaries, bibliographies http://im.bas-net.by/mathlib/en/ams.phtml?parent=55-XX

42. Dror Bar-Natan:Classes:2001-02:Algebraic Topology Fundamental Concepts in algebraic topology. Instructor Agenda Learn how algebraand topology interact in the field of algebraic topology. Syllabus http://www.math.toronto.edu/~drorbn/classes/0102/AlgTop/

Dror Bar-Natan Classes Fundamental Concepts in Algebraic Topology Instructor: Dror Bar-Natan drorbn@math.huji.ac.il Classes: Tuesdays 12:00-14:00 at Mathematics 110 and Thursdays 12:00-14:00 at Sprintzak 213. Review sessions: Thursdays 14:00-15:00 with Boris Chorny chorny@math.huji.ac.il Office hours: Tuesdays 14:00-15:00 in my office, Mathematics 309. Agenda: Learn how algebra and topology interact in the field of Algebraic Topology. Syllabus: Prerequisites: Point set topology and some basic notions of algebra - groups, rings, etc. Reading material: (each student must have a copy) Allen Hatcher 's Algebraic Topology (free download; a paper copy is available at my office for photocopying). Weekly Material: (Also use the primitive Class Notes Browser March 12, 14 Class notes for March 12th (the basic idea of algebraic topology, Brouwer's theorem, the fundamental group, the fundamental group of the circle). Homework assignment #1: Ex1.ps Ex1.png (category theory, fundamental group calculations, an application of Brouwer's theorem). Class notes for March 14th (the lifting property for covering spaces, the fundamental theorem of algebra, Brouwer's fixed point theorem)

43. KLUWER Academic Publishers | Algebraic K-Theory And Algebraic Topology Books » Algebraic KTheory and algebraic topology. Algebraic K-Theoryand algebraic topology. Add to cart. Proceedings of the NATO http://www.wkap.nl/prod/b/0-7923-2391-2

Title Authors Affiliation ISBN ISSN advanced search search tips Books Algebraic K-Theory and Algebraic Topology Algebraic K -Theory and Algebraic Topology Add to cart Proceedings of the NATO Advanced Study Institute, Lake Louise, Alberta, Canada, December 12-16, 1991 edited by P.G. Goerss University of Washington, Mathematics Dept., Seattle, USA J.F. Jardine Mathematics Dept., University of Western Ontario, London, Canada Book Series: NATO SCIENCE SERIES: C: Mathematical and Physical Sciences (continued within NATO SCIENCE SERIES II: Mathematics, Physics and Chemistry Volume 407 This book contains the proceedings of a conference entitled `Algebraic K K -theory and related developments in other fields. This book is intended for and will be of interest to researchers in K -theory, topology, geometry and number theory. Contents and Contributors Kluwer Academic Publishers, Dordrecht Hardbound, ISBN 0-7923-2391-2 July 1993, 340 pp. EUR 259.50 / USD 328.50 / GBP 198.00 Home Help section About Us Contact Us ... Search

44. KLUWER Academic Publishers | A User's Guide To Algebraic Topology Books » A User's Guide to algebraic topology. A User's Guide to AlgebraicTopology. Add to cart. by CTJ Dodson University of Toronto http://www.wkap.nl/prod/b/0-7923-4293-3

Title Authors Affiliation ISBN ISSN advanced search search tips Books A User's Guide to Algebraic Topology A User's Guide to Algebraic Topology Add to cart by C.T.J. Dodson University of Toronto, Ont., Canada Phillip E. Parker Wichita State University, KS, USA Book Series: MATHEMATICS AND ITS APPLICATIONS Volume 387 This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.

45. Sheafhom: Combinatorial Sheaves And Algebraic Topology Tools for computation in the category of combinatorial sheaves. It is intended for research involving Category Science Math Algebra Software......Sheafhom. Sheafhom is a set of tools for computation in the categoryof combinatorial sheaves. It is intended for research involving http://www.math.okstate.edu/~mmcconn/shh.html

Sheafhom Sheafhom is a set of tools for computation in the category of combinatorial sheaves. It is intended for research involving complexes of sheaves and the derived category. In principle, it can be used for any space topologically equivalent to a ranked poset; this includes the constructible derived category on arbitrary simplicial complexes and regular cell complexes. Sheafhom's main application so far is to toric varieties. The machine constructs the intersection cohomology complexes of sheaves (the IC sheaves) on an n -dimensional toric variety X , for any n and in any perversity. By taking hypercohomology, it finds the rational intersection cohomology ( IH ) of X . This includes the ordinary cohomology H ^* and homology H _* as special cases. It computes the canonical maps between IC sheaves, and the canonical intersection pairings, as well as the corresponding maps and pairings on IH ; as special cases, this includes the cup product on cohomology, and the H ^*-module structure (cap product) on IH in any perversity.

46. Algebraic Topology algebraic topology. What is topology? Well applications. Ok, so what's algebraictopology? Most branches of mathematics try to classify things. http://math.rice.edu/~gsclark/atop.html

Algebraic Topology What is topology? Well, in its most general form, topology tries to study properties such as connectedness and compactness, and how continuous maps preserve or these properties. A good way to think of topology is as "rubber geometry": doing geometry without worrying about distances or angles. It's like working with a piece of rubber, that you can mold and deform however you like, as long as you don't break it apart. As an example, a coffee cup and a donut are topologically equivalent; if you have a donut made of clay, you can deform it into a coffee cup. So what? It doesn't sound very useful. But most of the other branches of mathematics that you will ever encounter rely on topology. Analysis, of course, needs topology before you can even start doing analysis, the space you're working in needs a bunch of nice topological properties. Surprisingly enough, number theory uses topology as well. The p-adic numbers, for example, have a bunch of unusual topological properties. In addition to being an important foundation, a chemist has found a use

47. Algebraic Topology Authors/titles Recent Submissions Similar pages algebraic topologyalgebraic topology, Math 414b, Spring 2001. New addition check outAlan Hatcher's very nice book on algebraic topology. Algebraic http://xxx.lanl.gov/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

48. What Is Algebraic Topology? WHAT IS algebraic topology? THE BEGINNINGS OF algebraic topology. The winding numberof a curve illustrates two important principles of algebraic topology. http://www.math.rochester.edu/people/faculty/jnei/algtop.html

WHAT IS ALGEBRAIC TOPOLOGY? THE BEGINNINGS OF ALGEBRAIC TOPOLOGY Algebraic topology is a twentieth century field of mathematics that can trace its origins and connections back to the ancient beginnings of mathematics. For example, if you want to determine the number of possible regular solids, you use something called the Euler characteristic which was originally invented to study a problem in graph theory called the Seven Bridges of Konigsberg. Can you cross the seven bridges without retracing your steps? No and the Euler characteristic tells you so. Later, Gauss defined the so-called linking number, a precise invariant which tells you whether two circles are linked. It is called an invariant because it remains the same even if we continuously deform the geometric object. Gauss also found a relationship between the total curvature of a surface and the Euler characteristic. All of these ideas are bound together by the central idea that continuous geometric phenomena can be understood by the use of discrete invariants. The winding number of a curve illustrates two important principles of algebraic topology. First, it assigns to a geometric odject, the closed curve, a discrete invariant, the winding number which is an integer. Second, when we deform the geometric object, the winding number does not change, hence, it is called an invariant of deformation or, synomynously, an invariant of homotopy.

49. Algebraic Topology Click to enlage algebraic topology CRF Maunder. extremely valuable additionto the literature of algebraic topology. —The Mathematical Gazette. Unabr. http://store.doverpublications.com/0486691314.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Astronomy Biology and Medicine Bridge and Other Card Game...... Chemistry Chess Children Consumer Catalogs Cookbooks, Nutrition Crafts Detective Stories, Science...... Dover Phoenix Editions Earth Science Engineering Ethnic Interest Features Science Gift Certificates Gift Ideas Giftpack History, Political Science...... Holidays Humor Languages And Linguistics Literature Magic, Legerdemain Mathematics Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy And Religion Photography Physics Psychology Puzzles, Amusement, Recrea...... Reference Specialty Stores Sports, Out-of-door Activi...... Science and Mathematics Stationery, Gift Sets Summer Fun Shop Travel and Adventure Women's Studies By Subject Science and Mathematics Mathematics Topology Algebraic Topology C. R. F. Maunder Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes and other topics. Each chapter contains exercises and suggestions for further reading. 1980 corrected edition. Buy Now!

50. Algebraic Topology II algebraic topology II and III. Here are lecture notes. We have kansio 'san photocopy machines for that purpose. algebraic topology III. http://www.helsinki.fi/~korppi/alto2/

Algebraic topology II and III Here are some materials (lecture notes etc) for the courses Algebraic Topology II and III lectured by Sören Illman. Please do not use our university's printers to print lecture notes. We have "kansio"'s an photocopy machines for that purpose. Algebraic Topology III Proof that the modules of cycles and boundaries are free kanta.ps kanta.dvi The cardinality of a free set in a free Abelian group can not exceed the dimension. kh.ps My solution to the problem where the complement constsis of a finite number of cells. sama.ps Some exercises we made without Sören 7.3.2001 ratkasu.ps An element of a homotopy group has an inverse teese.ps Algebraic Topology II Lecture notes by Sören Illman (proofread by me; all the remaining mistakes are due to me.) alto2.dvi (New stuff 15.12.) alto2.ps (New stuff 15.12.) alto2.pdf (Temporarily unavailable) Appendix to the lecture notes by Sören Illman appen.dvi (New stuff 15.12.) appen.ps (New stuff 15.12.) Answers to exercises B3, B5 and B6 (by me) topo.dvi

51. MA4101 Algebraic Topology MA4101 algebraic topology. MA4101 algebraic topology. These ideas, andones like them, constitute the subject of algebraic topology. http://www.mcs.le.ac.uk/Modules/MA-02-03/MA4101.html

Next: MA4121 Projective Curves Up: Level 4 Previous: MA4021 Wavelets and Signal Processing MA4101 Algebraic Topology MA4101 Algebraic Topology Credits: Convenor: Dr. J. Hunton Semester: Prerequisites: essential: MA2151(=MC240), MA2102(=MC241), MA2111(=MC254) or MA2161(=MC255), MA3011(=MC355) desirable: Assessment: Coursework: 10% Three hour examination: 90% Lectures: Problem Classes: Tutorials: none Private Study: Labs: none Seminars: none Project: none Other: none Surgeries: none Total: Explanation of Pre-requisites This module will draw on some basic ideas from both algebra and analysis. In algebra familiarity with the basic concepts of vector spaces, as covered in MA2102, will also be assumed, as will some of the elementary ideas of abstract algebra such as groups, rings or modules, sub- and quotient objects, and so on, as discussed in MA2111 or MA2161. In analysis the central topics drawn on are those of topological spaces, of closed or compact subsets of and continuous functions. These are all covered in MA2151, but their presentation and the examples in MA3011 will probably be helpful in a number of ways. This module would make a good follow-on module from MA3011. Course Description Fact: if you have a dog which is completely covered in hair, then there is no way of combing that hair smooth so that there is no parting or bald spot. This is the so-called `hairy dog theorem'.

52. Mathematics 261: Algebraic Topology I . This course is an introduction to algebraic topology.......Mathematics 261 algebraic topology I (Spring 2003). Instructor. Paul Aspinwall. http://www.math.duke.edu/graduate/courses/spring03/math261.html

Mathematics 261: Algebraic Topology I (Spring 2003) Instructor Paul Aspinwall Description This course is an introduction to algebraic topology. A rough outline is as follows: Introductory ideas Basic ideas of category theory Homotopy Homotopy of maps Fundemental group Cell complexes Van Kampen's Theorem Covering spaces Higher homotopy groups (very briefly) Homology Chain complexes Simplicial homology Singular homology Relative homology Homotopy invariance Excision Mayer-Vietoris Sequence Cellular Homology Eilenberg-Steenrod Axioms Algebraic topology studies topological spaces by associating to them algebraic invariants. The principal algebraic invariants considered in this course are the fundamental group (also known as the first homotopy group) and the homology groups. This course is a prerequisite for Math 262 (Algebraic Topology II). It is fundamental for students interested in research in Algebraic Geometry, Differential Geometry, Mathematical Physics, and Topology; it is also important for students in Algebra and in Number Theory. Prerequisites Basic algebra (Math 200 or 251) and Topology (Math 205), or consent from me.

53. Mathematics 261: Algebraic Topology I . This course is an introduction to algebraic topology.......Mathematics 261 algebraic topology I (Spring 2002). Instructor. Paul Aspinwall. http://www.math.duke.edu/graduate/courses/spring02/math261.html

Mathematics 261: Algebraic Topology I (Spring 2002) Instructor Paul Aspinwall Description This course is an introduction to algebraic topology. A rough outline is as follows: Introductory ideas Basic ideas of category theory Homotopy Homotopy of maps Fundemental group Cell complexes Van Kampen's Theorem Covering spaces Higher homotopy groups (very briefly) Homology Chain complexes Simplicial homology Singular homology Relative homology Homotopy invariance Excision Mayer-Vietoris Sequence Cellular Homology Eilenberg-Steenrod Axioms Algebraic topology studies topological spaces by associating to them algebraic invariants. The principal algebraic invariants considered in this course are the fundamental group (also known as the first homotopy group) and the homology groups. This course is a prerequisite for Math 262 (Algebraic Topology II). It is fundamental for students interested in research in Algebraic Geometry, Differential Geometry, Mathematical Physics, and Topology; it is also important for students in Algebra and in Number Theory. Prerequisites Basic algebra (Math 200 or 251) and Topology (Math 205), or consent from me.

54. Research Group: Algebraic Topology And Group Theory Algebra and Topology Research Group.Category Science Math Topology Research Groups...... http://www.kulak.ac.be/facult/wet/wiskunde/algtop/

Next: Who and where are Sorry, this requires a browser that supports frames! Try index_ct.html instead. Paul Igodt

55. Algebra And Algebraic Topology Home Page School of Informatics, Algebra and algebraic topology.Category Science Math Topology Research Groups......Research Group Home Pages. Algebra algebraic topology. Introduction. ALGEBRAICTOPOLOGY AND HOMOLOGICAL ALGEBRA. A. Algebraic Models for Homotopy Types. http://www.informatics.bangor.ac.uk/public/mathematics/research/algtop/algtop2.h

University of Wales, Bangor - School of Informatics Research Group Home Pages Introduction. The research in algebra at Bangor has to a large extent been motivated by problems in algebraic topology and homological algebra. The recent spate of new and exciting concepts (crossed modules, crossed n-cubes, nonabelian tensor products, etc.) originating in those two areas has opened out many algebraic aspects of the theory and applications which are waiting to be investigated. Many final year pure mathematics courses have some Algebraic Topology in them. Typically the fundamental group and/or the homology groups are defined, studied and applied to various problems such as the existence of certain types of continuous maps, the classification of knots, and other problems of classification usually in low dimensions. These problems usually involve two basic questions: 1. How is one to tell if two spaces or two maps are "different"? 2. Can a map defined on part of a geometric object be extended to the whole of that object? In both cases the method of algebraic topology is to model certain important aspects of each space by some algebraic gadget, perhaps a group or a set of interrelated groups, use these to translate the problem to an algebraic context; try to solve that algebraic problem and finally to reinterpret the results back in terms of spaces.

56. Algebra And Algebraic Topology Algebra algebraic topology. The research in algebra at Bangor has to a large extentbeen motivated by problems in algebraic topology and homological algebra. http://www.informatics.bangor.ac.uk/public/mathematics/research/algtop/algtop1.h

University of Wales, Bangor School of Informatics Research Groups Page under construction Personnel: Prof Ronnie Brown Prof Tim Porter Dr Chris Wensley Collaborators: Introduction: The research in algebra at Bangor has to a large extent been motivated by problems in algebraic topology and homological algebra. The recent spate of new and exciting concepts (crossed modules, crossed n-cubes, nonabelian tensor products, etc.) originating in those two areas has opened out many algebraic aspects of the theory and applications which are waiting to be investigated. Current Projects: HOME PAGE of the research group. School of Informatics: home page Mathematics home page. U.W.Bangor Home Page Latest modification to this page: 10/ 5/00

57. Algebraic Topology algebraic topology. Although algebraic topology can be considered, by andlarge, as a creation of the 20th century, it has a long prehistory. http://www.maths.lth.se/matematiklu/personal/jaak/Alg-Top.html

Algebraic Topology Brief historical introduction Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long pre-history. It is generally considered to have its roots in Euler's polyhedron theorem (1752). This is the relation $$ E+F=K+2$$ where $E$ is the number of vertices, $K$ the number of edges, and $F$ the number of faces. In the first half of this century many mathematicians defined homology for more and more extended classes of topological spaces. Thus, for instance singular homology was first defined by Lefschetz in 1933. Finally, in 1945, Eilenberg and Steenrod developed an axiomatic approach to homology. It turned out that within the class of all topological spaces the Eilenberg and Steenrod axioms uniquely characterize singular homology. A parallel development took place in homotopy. Thus, higher homotopy groups were defined by Hurewicz in 1935 and their properties were developed. In the 1950's several new concepts were invented such as cobordism and $K$-theory. The course will be based mainly on Greenberg and Harper's book quoted below.

58. Algebraic Topology Notes Rob Thompson Department of Mathematics and Statistics Hunter College and GSUC,CUNY. These are the notes for my first year algebraic topology Course. http://math.hunter.cuny.edu/thompson/algtop/

Rob Thompson Department of Mathematics and Statistics Hunter College and GSUC, CUNY These are the notes for my first year Algebraic Topology Course. They are fairly rough, but you are invited to use them as you see fit. Presently, I have a dvi file and a pdf, so you will need a dvidriver or pdf reader. I hope to produce an HTML version, but that hasn't been done. algtop.dvi algtop.pdf

59. Mathematics Online Compendium: Algebraic Topology Catalogue of Algebraic Systems algebraic topology http//www.math.niu.edu/~rusin/papers/known-math/algebraic.top/,Last update January 18th, 1999. http://www.dei.unipd.it/~cuzzolin/MOCalgebraic.html

Catalogue of Algebraic Systems - Algebraic Topology http://www.math.niu.edu/~rusin/papers/known-math/algebraic.top/ Last update: January 18th, 1999

60. PMA 333 Algebraic Topology algebraic topology PMA 333. This course is taught by Neil Strickland. My officeis J10 in the Hicks Building, and my internal phone number is 23852. http://www.shef.ac.uk/~pm1nps/courses/algtop/

Algebraic Topology PMA 333 This course is taught by Neil Strickland. My office is J10 in the Hicks Building, and my internal phone number is 23852. The best way to reach me outside of lectures is by email: N.P.Strickland@sheffield.ac.uk. Lectures are at 11:10 on Tuesdays in Hicks lecture room 6, and at 11:10 on Fridays in Hicks lecture room 9. Problem sheets and solutions will appear on this web page in due course. Course information: The syllabus, recommended books, etc. Notes Pictures and animated diagrams The plane The sphere The torus The The projective plane Curves in a plane region Curves in the complement of a circle Path lifting Odds and ends Problem sets and solutions Problem set 1 and solutions Problem set 2 and solutions Problem set 3 and solutions Problem set 4 Problem set 5 About the exam A sample exam and solutions A collection of questions taken from past papers (and edited to make them compatible with this year's course) and solutions. You are warned that the sample exam and questions from past papers have not been thoroughly debugged.

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