Geometry.Net - Pure_And_Applied_Math: Algebraic Topology

Allen Hatcher's Homepage
A downloadable textbook in algebraic topology. This is the first in a series of three textbooks in algebraic topology having the goal of covering all
http://www.math.cornell.edu/~hatcher/

Extractions: On This Webpage: Book Projects: Algebraic Topology Vector Bundles and K-Theory Spectral Sequences in Algebraic Topology ... Books by other authors Book Projects Real and Imaginary This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature. The other two books, 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
AMS Online Books/COLL27
algebraic topology text published by the American Mathematical Society (AMS), and available as a free download in PDF format. © 1942 by Solomon Lefschetz,
http://www.ams.org/online_bks/coll27/
Algebraic Topology Discussion List
The primary functions of this list are 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. The site also serves as 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
55: Algebraic Topology
Encyclopedic reference for algebraic topology in Dave Rusin's Mathematical Atlas. Includes a brief history along with various links to textbooks, reference works, and tutorials on the subject.
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.)
Hopf Topology Archive, Revised Version
algebraic topology and related areas. (~400 articles)
http://hopf.math.purdue.edu/

Extractions: NOTICE: Hopf has been moved to a virtual website on the Math department server. Most things should be transparent if you use http://hopf.math.purdue.edu as the URL. The FTP service will not be reactivated due to security concerns. If you experience problems, please report them to wilker@math.purdue.edu Thank you. Hopf Author/Title Search: enter author or title keyword into box below. PaperSearch This archive list is current through August 2004 . Newer files may be in the proper directories but not listed on the html list. These are accessible as http://hopf.math.purdue/AuthorName Submitting Preprints and Uploading Preprints Latest maintained by Mark Hovey. Back issues of Mark's What's New!
Algebraic Topology Book
A complete, downloadable, introductory text on algebraic topology, by Prof. Allen Hatcher, Cornell Univ. 3rd Ed. 553 pp. with illustrations.
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 was published by Cambridge University Press in 2002. There are two editions: Electronic Version: By special arrangement with the publisher, an online version will continue to be available for download here. There are several different formats available. First of all, you can download the whole book as a single rather large pdf file (3.5MB) of about 550 pages. If you wish to save paper when you print it out, there is also a pdf
Algebraic Topology And Concurrency
Reports applying methods in algebraic topology to concurrent computation. Maintained by Stefan Sokolowski.
http://www.ipipan.gda.pl/~stefan/AlgTop/reports.html
AT Algebraic Topology
An archive of prepublication papers (preprints) on algebraic topology.
http://front.math.ucdavis.edu/math.AT
Open Problems In Algebraic Topology
Problems in algebraic topology, compiled by mathematician Mark Hovey of Wesleyan University.
http://claude.math.wesleyan.edu/~mhovey/problems/

Extractions: This list of problems is designed as a resource for algebraic topologists. The problems are not guaranteed to be good in any wayI just sat down and wrote them all in a couple of days. Some of them are no doubt out of reach, and some are probably even worseuninteresting. I ask that anybody who gets anywhere on any of these problems, has some new problems to add, or has corrections to any of them, please keep me informed (mhovey@wesleyan.edu). If I mention a name in a problem, it might be good to consult that person before working too hard on the problem. However, even if the problems we work on are internal to algebraic topology, we must strive to express ourselves better. If we expect our papers to be accepted in mathematical journals with a wide audience, such as the Annals, JAMS, or the Inventiones, then we must make sure our introductions are readable by generic good mathematicians. I always think of the French, myselfI want Serre to be able to understand what my paper is about. Another idea is to think of your advisor's advisor, who was probably trained 40 or 50 years ago. Make sure your advisor's advisor can understand your introduction. Another point of view comes from Mike Hopkins, who told me that we must tell a story in the introduction. Don't jump right into the middle of it with "Let E be an E-infinity ring spectrum". That does not help our field. Unstable modules and algebras over the Steenrod algebra (coming soon)
What Is Algebraic Topology?
Introductory essay by Joe Neisendorfer, University of Rochester.
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 -- From MathWorld
Index to more than 100 articles on algebraic topology.
http://mathworld.wolfram.com/topics/AlgebraicTopology.html
Algebraic Topology - Wikipedia, The Free Encyclopedia
An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning algebraic topology and
http://en.wikipedia.org/wiki/Algebraic_topology

Extractions: Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces edit The goal is to take topological spaces and further categorize or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space X was constructed from simpler ones. The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants, by mapping them, for example, to groups which have a great deal of manageable structure in a way that respects the relation of homeomorphism of spaces. Two major ways in which this can be done are through fundamental groups , or more generally homotopy theory , and through homology and cohomology groups. The fundamental groups give us basic information about the structure of a topological space, but they are often nonabelian and can be difficult to work with. The fundamental group of a (finite)
Algebraic Topology And Distributed Computing
Powerpoint tutorials by Maurice Herlihy at Brown University.
http://www.cs.brown.edu/people/mph/topology.html
Algebraic Topology & Concurrency
A collection of preprints on the applications of algebraic topology to Computer Science, such as the use of topological techniques to formulate synchronous
http://www.ipipan.gda.pl/~stefan/AlgTop/
Nantes 3-7 Sept 2001
University of Nantes, France; 37 September 2001.
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
Encyclopedic reference for _QUOTATION_algebraic topology_QUOTATION_ in Dave Rusin's Mathematical Atlas. Includes a brief history along with various
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
What Is Topology?
We can analyse the structure of Y using the methods of algebraic topology, and learn a number of interesting and nontrivial things about it.
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Algebraic Geometric Topology
Colin Rourke Brian Sanderson. Algebraic Geometric Topology ISSN 14722739 (on-line) 1472-2747 (printed) Algebraic Geometric Topology
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Essays About Algebraic Topology
Essays about algebraic topology. Survey articles for the general public algebraic topology entry in Wikipedia (online encyclopedia)
http://www.lehigh.edu/~dmd1/essays.html
AMS Summer 1999 Research Conference In Algebraic Topology
University of Colorado, Boulder, USA; 2024 June 1999. Photos, proceedings.
http://www.math.wayne.edu/~rrb/Summer99/

Extractions: HOMOTOPY METHODS IN ALGEBRAIC TOPOLOGY WHEN: Sunday, June 20 - Thursday, June 24, 1999 (check in June 19, check out June 25) WHERE: University of Colorado , Boulder, CO Now that the conference is over, this web page will be maintained for a time as a source of information about the conference and about the proceedings of the conference. (Which should be appearing any day now.) Here are some photos from the banquet, taken by Donna Salter of the AMS. Here is a copy of the conference photo . It is a 700500 byte jpeg, 3000 x 2187 pixels in size, which takes 10 to 20 minutes to download on my 28 K line. Note that the upper left corner is quite dark: there is nothing wrong with your browser. Scroll down and right to see the people in the photo. Here is a cropped version which is only 532849 bytes, 1265 x 436 pixels in size, and which appears much smaller for some reason known only to XV, the program used to crop it. This is the schedule of talks as they actually occurred, and an alphabetical list of speakers (with titles and abstracts), and the

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