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Algebraic Topology: more books (100)

A User's Guide to Algebraic Topology (Mathematics and Its Applications) by C.T. Dodson, P.E. Parker, et all 1997-01-31

Algebraic Topology (EMS Textbooks in Mathematics) by Tammo Tom Dieck, 2008-09-15

Differential Algebraic Topology (Graduate Studies in Mathematics) by Matthias Kreck, 2010-05-04

Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley, 2005-07-01

Algebraic Topology: A First Course (Mathematics Lecture Note Series) by Marvin J. Greenberg, John R. Harper, 1981-01-22

Algebraic Topology via Differential Geometry (London Mathematical Society Lecture Note Series) by M. Karoubi, C. Leruste, 1988-01-29

Lectures on algebraic topology (Mathematics lecture note series) by Marvin J Greenberg, 1967

Introduction to Differential and Algebraic Topology (Texts in the Mathematical Sciences) by Yu.G. Borisovich, N.M. Bliznyakov, et all 2010-11-02

Algebraic Topology by Robert M. Switzer, 2002-02-26

Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series) by Albrecht Pfister, 1995-10-27

Foundations of Algebraic Topology (Mathematics Series) by Samuel Eilenberg, Norman E. Steenrod, 1952-12

Homology Theory: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (v. 145) by James W. Vick, 1994-01-07

Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin, 2008-02-04

A Combinatorial Introduction to Topology by Michael Henle, 1994-03-14

lists with details

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
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/

Extractions: Dror Bar-Natan Classes 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) 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).
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
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

Extractions: 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.
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 SoftwareSheafhom. 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

Extractions: 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.
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

Extractions: 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. 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
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
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

Extractions: 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.
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

Extractions: 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 (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.
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/

Extractions: 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. The cardinality of a free set in a free Abelian group can not exceed the dimension. My solution to the problem where the complement constsis of a finite number of cells. Some exercises we made without Sören 7.3.2001 An element of a homotopy group has an inverse Appendix to the lecture notes by Sören Illman Answers to exercises B3, B5 and B6 (by me) topo.dvi
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

Extractions: Next: MA4121 Projective Curves Up: Level 4 Previous: MA4021 Wavelets and Signal Processing 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: 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. 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'.
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

Extractions: Paul Aspinwall This course is an introduction to algebraic topology. A rough outline is as follows: Homotopy Homology 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. Basic algebra (Math 200 or 251) and Topology (Math 205), or consent from me.
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

Extractions: Paul Aspinwall This course is an introduction to algebraic topology. A rough outline is as follows: Homotopy Homology 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. Basic algebra (Math 200 or 251) and Topology (Math 205), or consent from me.
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/
Algebra And Algebraic Topology Home Page
School of Informatics, Algebra and algebraic topology.Category Science Math Topology Research GroupsResearch 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

Extractions: 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: 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.
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

Extractions: Page under construction 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. 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
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

Extractions: 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.
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/

Extractions: 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
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
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/

Extractions: 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.

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