41. Allen Hatcher's Homepage Links to online texts and papers (published and unpublished) on Algebraic Topology, KTheory, and 3-Manifolds. http://www.math.cornell.edu/~hatcher/

Allen Hatcher Office: 553 Malott Hall Phone: (607)-255-4091 Book Projects: Algebraic Topology Vector Bundles and K-Theory Spectral Sequences in Algebraic Topology ... Topology of Numbers Course Notes: Basic 3-Manifold Topology Introductory Point-Set Topology Papers Other Things: Pictures of stable homotopy groups of spheres Pictures of the cohomology of SO(n) List of recommended books in Topology (from 2003, needs updating) Books by other authors Book Projects Algebraic Topology This is the first in a planned 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 second and third books 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 intention 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

42. University Of Chicago Algebraic Topology Seminar To request a future speaker or for questions, please contact Vigleik Angeltveit (vigleik AT math.uchicago.edu). To sign up for electronic announcements of talks, please visit http://www.math.uchicago.edu/~vigleik/topcal.cgi

University of Chicago Algebraic Topology Seminar Algebraic Topology Seminar Location: Room 203 in Eckhart Hall Directions Day: Tuesdays Time: Pretalk at 3:00, Talk at 4:30 (unless otherwise specified) Practical Information for speakers To request a future speaker or for questions, please contact Vigleik Angeltveit (vigleik AT math.uchicago.edu). To sign up for electronic announcements of talks, please visit http://zaphod.uchicago.edu:8080/mailman/listinfo/topology Here is a link to the proseminar Autumn 2010 Seminars 4:30 pm Tuesday, September 28, 2010 in E203 Algebraic Topology Duality for Topological Modular Forms by Vesna Stojanoska (Northwestern) It has been observed that certain localizations of the spectrum of topological modular forms tmf are self-dual (Mahowald-Rezk, Gross-Hopkins). We provide an integral explanation of these results that is internal to the geometry of the (compactified) moduli stack of elliptic curves M, yet is only true in the derived setting. When 2 is inverted, choice of level-2-structure for an elliptic curve provides a geometrically well-behaved cover of M, which allows one to consider tmf as the homotopy fixed points of tmf(2), topological modular forms with level-2-structure, under a natural action by GL_2(Z/2). As a result of Grothendieck-Serre duality, we obtain that tmf(2) is self dual. The vanishing of the associated Tate spectrum then makes tmf itself Anderson self-dual. 4:30 pm Tuesday, October 5, 2010 in E203

43. PlanetMath: Bibliography For Groupoids And Algebraic Topology The following are recent sources for several areas in abstract algebra, homological algebra, homotopy groups, homotopy groupoids, algebraic topology and higher dimensional algebra (HDA) http://planetmath.org/encyclopedia/BibliographyForGroupoidsAndAlgebraicTopology.

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About bibliography for groupoids and algebraic topology (Bibliography) The following are recent sources for several areas in abstract algebra , homological algebra, homotopy groups homotopy groupoids algebraic topology and higher dimensional algebra (HDA). Algebraic Topology and Groupoids Ronald Brown: Topology and Groupoids , BookSurge LLC (2006). Ronald Brown R, P.J. Higgins, and R. Sivera.: ``Non-Abelian algebraic topology" . http://www. bangor.ac.uk/mas010/nonab-a-t .html ; http://www.bangor.ac.uk/mas010/nonab-t/partI010604.pdf , Springer: in press (2010). R. Brown and J.-L. Loday: Homotopical excision, and Hurewicz theorems , for n-cubes of spaces, Proc. London Math. Soc., 54:(3), 176-192, (1987). R. Brown and J.-L. Loday: Van Kampen Theorems for

44. Front: Math.AT Algebraic Topology An archive of pre-publication papers (preprints) on Algebraic Topology. http://front.math.ucdavis.edu/math.AT

Front for the arXiv Fri, 29 Oct 2010 Front math AT search register submit journals ... iFAQ math.AT Algebraic Topology Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 28 Oct arXiv:1010.5635 The Segal conjecture for topological Hochschild homology of complex cobordism. Sverre LunøeNielsen , John Rognes math.AT 28 Oct arXiv:1010.5633 The topological Singer construction. Sverre LunøeNielsen , John Rognes math.AT 27 Oct arXiv:1010.5269 The Mayer-Vietoris Property in Differential Cohomology. James Simons , Dennis Sullivan math.AT math.DG math.QA Cross-listings 29 Oct arXiv:1010.6039 A pull-back procedure of the Gromoll-Meyer construction. Llohann D. Sperança math.DG math.AT math.GT 27 Oct arXiv:1009.0793 Notes on noncommutative algebraic topology. Igor Nikolaev math.OA math.AT Revisions 29 Oct arXiv:1009.3622 The homotopy type of toric arrangements. Luca Moci , Simona Settepanella math.AT math.GT math.RT 29 Oct arXiv:1005.4878 Azumaya Objects in Bicategories. Niles Johnson math.AT math.CT math.RA 28 Oct arXiv:0906.0245

45. Algebraic Topology For Dummies? Algebraic topology for dummies? Science Book Discussion discussion http://www.physicsforums.com/showthread.php?t=198864

46. Open Problems In Algebraic Topology Problems in Algebraic Topology, compiled by mathematician Mark Hovey of Wesleyan University. http://claude.math.wesleyan.edu/~mhovey/problems/

Mark Hovey's Algebraic Topology Problem List 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. Here are the problems: Major problems in the field Morava K- and E-theory Elliptic cohomology Applications ... Miscellaneous Unstable modules and algebras over the Steenrod algebra (coming soon)

47. Algebraic Topology: Definition From Answers.com The study of topological properties of figures using the methods of abstract algebra; includes homotopy theory, homology theory, and cohomology theory. http://www.answers.com/topic/algebraic-topology

48. Algebraic Topology -- From Wolfram MathWorld Index to more than 100 articles on Algebraic Topology. http://mathworld.wolfram.com/topics/AlgebraicTopology.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Topology Algebraic Topology Absolute Retract Homeomorphism Group Relative Homotopy Group Abstract Simplicial Co... ... Quillen-Lichtenbaum Co...

49. Algebraic Topology -- From Wolfram MathWorld Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that http://mathworld.wolfram.com/AlgebraicTopology.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Derwent Algebraic Topology Algebraic topology is 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 Algebraic topology originated with combinatorial topology , but went beyond it probably for the first time in the 1930s when was developed. A technical way of saying this is that algebraic topology is concerned with functors from the topological category of groups and homomorphisms . Here, the

50. Algebraic Topology, Homotopy Theory - Math.umn.edu Mark Feshbach feshbach@math.umn.edu Professor , Ph.D. 1976 Stanford University algebraic topology . David Frank frank@math.umn.edu http://www.math.umn.edu/grad/areas/alg_top.html

Institute of Technology One Stop Directories Search U of M ... Graduate Program Algebraic Topology, Homotopy Theory math page grad page research page Mark Feshbach feshbach@math.umn.edu Professor , Ph.D. 1976 Stanford University algebraic topology David Frank frank@math.umn.edu Associate Professor , Ph.D. 1967 University of California Berkeley algebraic topology Donald Kahn kahn@math.umn.edu Professor , Ph.D. 1961 Yale University algebraic topology, global analysis Tyler Lawson talwson@math.umn.edu Assistant Professor , Ph.D. 2004, Stanford University algebraic topology, K-theory Alexander Voronov voronov@math.umn.edu Professor , Ph.D. 1988, Moscow State University math physics, algebra, algebraic geometry, algebraic topology Peter Webb webb@math.umn.edu Professor , Ph.D. 1979 Queen Mary College, London representation theory of groups and algebras, algebraic topology, combinatorics, category theory Director of Graduate Studies in Mathematics 127 Vincent Hall 206 Church St. S.E. Minneapolis, MN 55455 USA URL http://www.math.umn.edu/grad/areas/alg_top.html The University of Minnesota is an equal opportunity educator and employer.

51. Algebraic Topology Definition Of Algebraic Topology In The Free Online Encyclope algebraic topology. Field of mathematics that uses algebraic structures to study transformations of geometric objects. It uses function s (often called maps in this context) to http://encyclopedia2.thefreedictionary.com/algebraic topology

52. ALGTOP-L, Algebraic Topology Listserv 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

ALGTOP-L, Algebraic Topology listserv This listserv began as a discussion group in July 1995, and was converted to an automated moderated listserv in Sept 2007. To join the listserv or use it, go to https://lists.lehigh.edu/mailman/listinfo/algtop-l The primary functions of this listserv are providing information about topology conferences and jobs, 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 Mark Hovey. It has been largely replaced by the arXiv Information about conferences Messages posted to the Discussion Group 1998-Sept. 2007 . The postings to the listserv are archived on the listserv. Anyone, including nonmembers, can read them here To obtain a list of our subscribers' e-mail addresses, you must now join the listserv, where this information is readily available. Links to other sites related to algebraic topology (books, journals, tables, research groups, ongoing seminars, other sites) As a service for the nonspecialist, we have an

53. Algebraic Topology - Cambridge University Press For price and ordering options, inspection copy requests, and reading lists please select Europe, Middle East and Africa Americas Asia Australia and New Zealand http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521080767

54. Algebraic Topology - Cambridge University Press Paperback (ISBN13 9780521795401 ISBN-10 0521795400) There was also a Hardback of this title but it is no longer available; Published April 2002 http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=9780521795401

55. Algebraic Topology Article on Algebraic Topology New! You can click on formulas to copy the LaTeX source to your clipboard. Math Videos http://myyn.org/m/article/algebraic-topology/

56. K-theory Preprint Archives An extensive archive of pre-publication papers (preprints) on Algebraic K-Theory. http://www.math.uiuc.edu/K-theory/

57. 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 http://www.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

58. K-theory Calendar A calendar of upcoming and past events (workshops, colloquia, lectures) pertaining to K-Theory and its applications. http://www.math.uiuc.edu/K-theory/Calendar/

K-theory Calendar Instructions To get your K-theory event listed here and/or sent out to the K-theory preprint archives mailing list, send email to Dan Grayson Related sites Midwest Topology Seminar The future , November 1 - 5, 2010, K-Theory, C*-Algebras and Index Theory Los Angeles , March 22 - 25, 2011, Conference on K-theory and motives , dedicated to Andrei Suslin's 60th birthday. The past Bonn , September 6 - 10, 2010, Geometric aspects of motivic homotopy theory Buenos Aires , July 26-August 6, 2010, NCG School: Topics in Non Commutative Geometry Barcelona , July 12 - 22, 2010, Regulators III St. Petersburg , June 25 - 29, 2010, Algebraic Geometry, Algebraic K-theory, and Motives , dedicated to Andrei Suslin's 60th birthday. Lens , June 14 - 18, 2010, Linear Algebraic Groups and Quadratic Forms: Patching, Involutions and Buildings , May 7 - 8, 2010, Thirteenth NRW Topology Meeting Ottawa , March 26 - 28, 2010, Torsors, Lie algebras and Galois cohomology Columbus , November 7 - 8, 2009, Algebraic Cycles III: a follow-up workshop Mainz , October 29 - 30, 2009, Pfister forms , October 8 - 10, 2009, a conference on Combinatorial structures in algebra and topology Loen, Norway

59. MIT Mathematics | Algebraic Topology Algebraic Topology. The notion of shape is fundamental in mathematics. Geometry concerns the local properties of shape such as curvature, while topology involves largescale http://www-math.mit.edu/research/pure/algtop.html

skip to content Search Sitemap Contact Us About Us Welcome ... Summer Programs selSection('research'); Pure Algebraic Topology Geometry Number Theory ... Reading Room Algebraic Topology Our department has played a seminal role in this line of research, which has now flowered into a major discipline itself. MIT faculty and instructors have gone on to make connections with still more elaborate and contemporary segments of arithmetic algebraic geometry, and are now in the process of reworking this entire area, creating a deep unification of algebraic geometry and algebraic topology. This work will form the foundation of much research over the next decade, and offers the promise of providing tools useful in algebra as well as in topology. Specifically, our group works in stable and unstable homotopy theory, homotopical group theory, higher category theory, derived algebraic geometry, elliptic cohomology, computational homotopy theory and string topology. Research and Training Group Research and training in Geometry and Topology, from the undergraduate to the postdoctoral level, are supported by an RTG grant from the National Science Foundation. For more information about the various RTG activities, see the RTG website Faculty Clark Barwick Mark Behrens Haynes Miller Massachusetts Institute of Technology Department of Mathematics math@mit.edu

60. An Introduction To Algebraic K-theory An incomplete graduate textbook in Algebraic K-Theory, by Charles Weibel. Several chapters are available online. http://math.rutgers.edu/~weibel/Kbook.html

``The K-book: An introduction to algebraic K-theory'' by Charles Weibel (a graduate textbook in progress) Introduction here . (These are .dvi files) Chapter I : Projective Modules and Vector Bundles Here is the corresponding .dvi file Last major update March 1997. Minor updates July 2000, Sept. 2004, June 2005, May 2007, November 2008. 1. Free and stably free modules; p.1 2. Projective modules; p.6 3. The Picard group of a ring; p.15 4. Topological vector bundles and Chern classes; p.26 5. Algebraic vector bundles; p.38 Chapter II : The Grothendieck group K_0 (101 pp.) Here is the corresponding .dvi file Last major updates Dec. 2003 (sec.6, 7, 9), July 2004 (sec.2, 7, App.). Minor updates Sept. 2004, June 2005 (sec.3), August 2006 (Burnside ring), Jan 2007 (compatibility with Chapter V). 1. group completion of a monoid; p.1 2. K_0 of a ring; p.5 3. K(X) of a topological space; p.17 Lambda and Adams operations; p.24 5. K_0 of a symmetric monoidal category; p.37 6. K_0 of an abelian category; p.45 7. K_0 of an exact category; p.59

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