21. SpringerLink - K-Theory, Volume 38, Number 2 springerlink.metapress.com/content/15730514/PlanetMath k-theoryTopological k-theory is a generalised cohomology theory on the category of compact Hausdorff spaces. It classifies the vector bundles over a space $X$ up to http://springerlink.metapress.com/content/1573-0514/

Username Password Remember Me Forgot your Password? Register Now Log In via Shibboleth or Athens SpringerLink Skip to Main Content Log In or Out Skip to Search springer.com ... springerprotocols.com Choose preferred language English Deutsch SpringerLink You have Guest access. What can I do as a guest? Search Basic Search Search For All Content Author or Editor Publication Volume Issue Page Advanced Search Content Search For Full Text Title Only DOI Author Editor Citation Publication (Title, DOI ISSN or ISBN Volume Issue Page Category and Date Limiters Content Category All Categories Only Journals Only Books Only Protocols Entire Range of Publication Dates Select date range Publication Dates Between Start Date AND End Date Order of Results Most Relevant First Most Recently Published First Alphabetical Home My SpringerLink Saved Items Favorites ... Mathematics and Statistics K-Theory Volume 1 / 1987 - Volume 38 / 2008 Volume 38 , Number 2 / January 2008 Viewing all 8 articles Journal About Search within Search Within This Journal Hide Filters Show Filters Browse This Journal Online First™ Open Access Samples Contemporary Content Volume 38 Number 2 / January 2008 Number 1 / November 2007 Volume 37 Number 4 / April 2006 Number 3 / March 2006 ... Number 1 / January 1997 Archival Content Volume 10 / 1996 (6 Issues) Volume 9 / 1995 (6 Issues) Volume 8 / 1994 (6 Issues) Volume 7 / 1993 (6 Issues) ... Volume 1 / 1987-1988 (6 Issues) About This Journal Title K-Theory Coverage Volume 1 / 1987 - Volume 38 / 2008 Collection Mathematics and Statistics Subjects

22. Lectures On Topological K-theory This will be an expository seminar on the elements of topological ktheory at a level suitable for graduate students in mathematics and physics. http://online.itp.ucsb.edu/online/ktheory/

HOME DIRECTORY FOR SCIENTISTS TALKS ... HELP Oct 30, 2010 Lectures on Topological K-theory ITP Small Seminar Room Fridays at 3:30 pm, Spring 2000 Friday, April 7, Xianzhe Dai, Introduction [Audio] Friday, April 14, Siye Wu, The Grothendieck construction [Audio] Friday, April 21, Bill Jacob, Algebraic K-theory (first steps) [Audio] Friday, April 28, Doug Moore, K-theory and cohomology Friday, May 5, Rick Ye, The Bott periodicity theorem [Audio] Friday, May 12, Joe Polchinski, D-branes and K-theory [Audio] Friday, May 19, Simeon Hellerman, D-branes and K-theory II [Audio] Friday, May 26, Morten Krogh, Ramond-Ramond fields and K-theory I [Audio] Friday, June 2, Morten Krogh, Ramond-Ramond fields and K-theory II [Audio] Friday, June 9, Siye Wu, K-theory, T-duality and D-brane anomalies [Audio] This will be an expository seminar on the elements of topological K-theory at a level suitable for graduate students in mathematics and physics. Just like the fundamental group and the de Rham cohomology groups, K-theory provides topological invariants of smooth manifolds. These topological invariants are constructed from isomorphism classes of vector bundles over manifolds. Among its early applications to topology was a simple proof of the fact that the only spheres which possess trivial tangent bundles are those of dimensions 1,3 and 7. It was also one of the key tools used by Atiyah and Singer in their index theorem for systems of elliptic partial differential equations on smooth manifolds. More recently K-theory has become an important ingredient in the theory of D-branes from theoretical physics.

23. K-theory Calendar A calendar of upcoming and past events (workshops, colloquia, lectures) pertaining to ktheory 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

24. RTN Network K-Theory And Algebraic Groups TMR Network Project. Network Coordinator Ulf Rehmann, Bielefeld. http://www.math.uni-bielefeld.de/K AG/

25. K-theory ktheory The topic of k-theory spans the subjects of algebraic topology, abstract algebra and some areas of application like operator algebras and algebraic geometry. http://www.fact-index.com/k/k_/k_theory.html

Main Page See live article Alphabetical index K-theory The topic of K-theory spans the subjects of algebraic topology abstract algebra and some areas of application like operator algebras and algebraic geometry . It leads to the construction of families of K-functors, which contain useful but often hard-to-compute information. The subject takes its name from a particular construction applied by Alexander Grothendieck in his proof of the Riemann-Roch theorem . In it, a commutative monoid of sheaves of abelian groups under direct sum was converted into a group, by the formal addition of inverses (an explicit way of explaining a left adjoint ). This construction was taken up by Atiyah and Hirzebruch to define K(X) for a topological space X , by means on the analogous sum construction for vector bundles. This was the basis of the first of the extraordinary cohomology theories of algebraic topology . It played a big role in the proof around 1962 of the Index Theorem In turn, Jean-Pierre Serre used the analogy of vector bundles with projective modules to found in 1959 what became algebraic K-theory . He made Serre's conjecture , that projective modules over the ring of polynomials over a field are free modules; this resisted proof for 20 years.

26. LMS K-theory Days The 49th ktheory Day, sponsored by the London Mathematical Society, will take place in Oxford on 11th November 2008. The programme will be as follows http://www.personal.soton.ac.uk/jb32/Ktheory/

K-theory Days by Jacek Brodzki The LMS is kindly sponsoring a series of collaborative seminars in K-theory and Analysis under the Scheme 3. This seminar meets at least four times per year and is organised by J. Brodzki (Southampton) R. Plymen (Manchester) U.Tillmann (Oxford) The Next K-theory Day The 49th K-theory Day, sponsored by the London Mathematical Society, will take place in Oxford on 11th November 2008 . The programme will be as follows: Thomas Schick, Goettingen A K-theoretic codimension 2 obstruction to positive scalar curvature. Siegfried Echterhoff, Muenster Fibrations with non-commutative fibres. Richard Szabo, Heriot-Watt D-branes, duality and noncommutative correspondences. Programmes of past K-theory Days The 47th and 48th K-theory Days were combined to form a special event to celebrate Roger Plymen's 65th birthday. This event, which took place in Manchester, was sponsored by grants from the EPSRC, the LMS and from MIMS. The programme was as follows: Thursday, 10 July 2008.

27. K-theory Summary | BookRags.com ktheory. k-theory summary with 2 pages of encyclopedia entries, research information, and more. http://www.bookrags.com/wiki/K-theory

28. K-theory In NLab May 31, 2010 ktheory starts with the study of these K-groups and their higher analogues. Sometimes the K-groups themseles are called �k-theory�. http://ncatlab.org/nlab/show/K-theory

nLab K-theory Skip the Navigation Links Home Page All Pages Recently Revised ... fiber sequence /long sequence in cohomology principal ∞-bundle associated ∞-bundle Special and general types cochain cohomology singular cohomology group cohomology nonabelian group cohomology ... hypercohomology Variants equivariant cohomology equivariant homotopy theory Bredon cohomology twisted cohomology ... twisted differential String- and Fivebrane structures differential cohomology differential generalized (Eilenberg-Steenrod) cohomology differential cobordism cohomology Deligne cohomology differential K-theory ... relative cohomology Operations cup product fiber integration orientation transgression Theorems de Rham theorem Brown representability theorem Edit this sidebar Contents Idea Special cases and models Definition Related entries ... References Idea Given a stable (∞,1)-category C , its decategorification K C equivalence classes c of objects c C naturally inherits the structure of an abelian group from the fibration sequence s in C for a x c a fibration sequence (i.e. a homotopy exact sequence) the abelian group operation K C K C K C is such that x a c The group K C is called the K-group of C or the Grothendieck group of C . See in particular the latter entry for more details. The “K” is chosen by Grothendieck for the German word Klasse for “class”. The K-group of

29. Algebraic K-theory, 2004 The topics covered at this meeting will include the most recent developments in algebraic ktheory and the closely allied areas of motivic homotopy theory, http://www.math.uwo.ca/~jardine/CRM2004.html

Algebraic K-theory, 2004 October 2-6, 2004 The topics covered at this meeting will include the most recent developments in algebraic K-theory and the closely allied areas of motivic homotopy theory, algebraic cycles, and motivic cohomology theory, along with applications in other areas of Mathematics. The following mathematicians have agreed to speak: Gunnar Carlsson (Stanford) Thomas Geisser (USC) Alexander Goncharov (Brown) Jens Hornbostel (Regensburg) Max Karoubi (Paris VII) Marc Levine (Northeastern) Ib Madsen (Aarhus) Fabien Morel (Munich LMU) Markus Rost (Bielefeld) Marco Schlichting (LSU) R. Sujatha (Tata Institute) Andrei Suslin (Northwestern) Burt Totaro (Cambridge) Mark Walker (Nebraska) Kirill Zainoulline (Bielefeld) Housing and travel information, and an online registration form are available at the CRM conference page Abstracts for the lectures at this meeting are available here Here is a schedule of the lectures. This conference has been funded by grants from the CRM and National Science Foundation. Some travel support will be available for graduate students and junior researchers. The organizers for this meeting are: Rick Jardine jardine@uwo.ca

30. NII-REO K-Theory reo.nii.ac.jp/journal/HtmlIndicate/html/vol_issues/ /vol_issue_list.htmlConference on ktheory and Homotopy TheoryCall for Papers Special Issue of the Journal of Homotopy and Related Structures (International Conference on k-theory and Homotopy Theory). Important Dates http://reo.nii.ac.jp/journal/HtmlIndicate/html/vol_issues/SUP0000004000/JOU00040

HOME K-Theory Volume 24 p.303-412 December 1, 2001 p.203-301 November 1, 2001 p.109-201 October 1, 2001 p.1-107 September 1, 2001 Volume 23 p.303-400 August 1, 2001 p.203-303 July 1, 2001 p.1-202 June 1, 2001 p.1-104 May 1, 2001 Volume 22 p.303-402 April 1, 2001 p.199-301 March 1, 2001 p.1-197 January 1, 2001 Volume 21 p.301-420 December 1, 2000 p.201-300 November 1, 2000 p.101-199 October 1, 2000 p.1-100 September 1, 2000 Volume 20 p.299-368 August 1, 2000 p.201-298 July 1, 2000 p.97-200 June 1, 2000 p.1-95 May 1, 2000 Volume 19 p.311-403 April 1, 2000 p.211-309 March 1, 2000 p.109-209 February 1, 2000 p.1-108 January 1, 2000

31. [math/0504555] K-theory And Elliptic Operators Abstract This expository paper is an introductory text on topological ktheory and the Atiyah-Singer index theorem, suitable for graduate students or advanced undegraduates http://arxiv.org/abs/math.AT/0504555

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: math new recent NASA ADS Bookmark what is this? Mathematics > Algebraic Topology Title: K-theory and elliptic operators Authors: Gregory D. Landweber (University of Oregon) (Submitted on 27 Apr 2005) Abstract: Comments: 50 pages Subjects: Algebraic Topology (math.AT) ; K-Theory and Homology (math.KT) MSC classes: Primary: 55N15, 58J20; Secondary: 19L47 Cite as: arXiv:math/0504555v1 [math.AT] Submission history From: Gregory D. Landweber [ view email Wed, 27 Apr 2005 19:27:05 GMT (45kb) Which authors of this paper are endorsers? Link back to: arXiv form interface contact

32. An Introduction To K-theory You will find here the text of 2 lectures comprising �An Introduction to K theory� given at the 38th meeting of the �Transpenine Topology Triangle� held in http://www-maths.swan.ac.uk/staff/fwc/IKT.html

An Introduction to K-theory University Mathematics Francis Clarke Research Interests ... Text An Introduction to K -theory IKT An Introduction to K-theory K th Transpenine Topology Triangle th The text of the lectures (pdf file) University Mathematics Francis Clarke Research Interests 18 October 2005 Webmaster

33. Guide To Math Used In String Theory These are topics in mathematics at the current cutting edge of superstring research. ktheory Cohomology is a powerful mathematical technology for http://www.superstringtheory.com/math/math3.html

The Official String Theory Web Site Mathematics These are topics in mathematics at the current cutting edge of superstring research. K-theory Cohomology is a powerful mathematical technology for classifying differential forms. In the 1960s, work by Sir Michael Atiyah, Isadore Singer, Alexandre Grothendieck, and Friedrich Hirzebruch generalized coholomogy from differential forms to vector bundles, a subject that is now known as K-theory Witten has argued that K-theory is relevant to string theory for classifying D-brane charges. D-brane objects in string theory carry a type of charge called Ramond-Ramond charge. Ramond-Ramond fields are differential forms, and their charges should be classifed by ordinary cohomology. But gauge fields propagate on D-branes, and gauge fields give rise to vector bundles. This suggests that D-brane charge classification requires a generalization of cohomology to vector bundles hence K-theory. Overview of K-theory Applied to Strings by Edward Witten D-branes and K-theory by Edward Witten Noncommutative geometry (NCG for short) Geometry was originally developed to describe physical space that we can see and measure. After modern mathematics was freed from Euclid's Fifth Axiom by Gauss and Bolyai, Riemann added to modern geometry the abstract notion of a manifold M with points that are labeled by local coordinates that are real numbers, with some metric tensor that determines an extremal length between two points on the manifold.

34. Trace Methods In Algebraic K-Theory Oct 3, 2003 Muenster, Germany; 29 September 3 October 2003. http://wwwmath.uni-muenster.de/u/varisco/tmakt/

Workshop on Trace Methods in Algebraic K-Theory Monday, September 29 to Friday, October 3, 2003 Program You may download an updated program of the workshop, with abstracts and schedule, in PostScript or PDF format. booklet photos Participants Organizers Lars Hesselholt (Massachusetts Institute of Technology), Location Mathematisches Institut (Germany). The workshop will be supported by the SFB 478 "Geometrische Strukturen in der Mathematik". Contact information Please send an email to the organizers Workshop on Topological Modular Forms More information Marco Varisco - September 25, 2003 http://www.math.uni-muenster.de /u/varisco /tmakt

35. K-theory - Definition The topic of ktheory spans the subjects of algebraic topology, abstract algebra and some areas of application like operator algebras and algebraic geometry. http://www.wordiq.com/definition/K-theory

K-theory - Definition The topic of K-theory spans the subjects of algebraic topology abstract algebra and some areas of application like operator algebras and algebraic geometry . It leads to the construction of families of K functors , which contain useful but often hard-to-compute information. The subject takes its name from a particular construction applied by Alexander Grothendieck in his proof of the Riemann-Roch theorem . In it, a commutative monoid of sheaves of abelian groups under direct sum was converted into a group, by the formal addition of inverses (an explicit way of explaining a left adjoint ). This construction was taken up by Atiyah and Friedrich Hirzebruch to define K X ) for a topological space X , by means on the analogous sum construction for vector bundles . This was the basis of the first of the extraordinary cohomology theories of algebraic topology . It played a big role in the proof around 1962 of the Index Theorem In turn, Jean-Pierre Serre used the analogy of vector bundles with projective modules to found in 1959 what became algebraic K-theory . He for formulated Serre's conjecture , that projective modules over the ring of polynomials over a field are free modules ; this resisted proof for 20 years.

36. Göttingen 2010: K-Theory, C*-Algebras And Index Theory ktheory, C*-Algebras and Index Theory. November 1 - 5, 2010 in G�ttingen DFG-RFBR network k-theory, C*-Algebras and Index Theory http://www.uni-math.gwdg.de/kcit/

K-Theory, C*-Algebras and Index Theory PROGRAM The registration is closed Registration fee: 30 Euro. The registration fee can be waved for active participants (speaker/poster). Participants Funding Limited funding is available to graduate students and postdoctoral fellows information on travel and accommodation Poster (pdf) Supported by - DFG-RFBR network "K-Theory, C*-Algebras and Index Theory" - the Courant Research Centre "Higher Order Structures in Mathematics" Speakers include: Paul Baum (Penn State) Dan Burghelea (Ohio State) Alexander Helemskii (Moscow) Yuri Kordyukov (Ufa) Julia Kuznetsova (Luxembourg) Alexander Mishchenko (Moscow) Andreas Thom (Leipzig) Stanislav Woronowicz (Warsaw) Organizers: Thomas Schick Mathematisches Institut Bunsenstr. 3-5 Michael Frank University of Applied Sciences (HTWK) Leipzig Evgenii Troitsky Alexander Mishchenko Alexander Pavlov Moscow State University for all enquiries please contact: Claudia Gabler

37. Ingentaconnect Publication: K-Theory ktheory. ISSN 0920-3036. k-theory logo Springer logo. Publisher Springer. 102 issues are available electronically. Volume 37; Number 4, April 2006 http://www.ingentaconnect.com/content/klu/kthe

38. Algebraic K-theory - Definition In mathematics, algebraic ktheory is an advanced part of homological algebra concerned with defining and applying a sequence K n (R) of functors from rings to abelian groups, for n = 0,1 http://www.wordiq.com/definition/Algebraic_K-theory

Algebraic K-theory - Definition In mathematics algebraic K-theory is an advanced part of homological algebra concerned with defining and applying a sequence K n R of functors from rings to abelian groups , for n = 0,1,2, ... . Here for traditional reasons the cases of K and K are thought of in somewhat different terms from the higher algebraic K-groups K n for n K generalises the construction of the ideal class group , using projective modules ; and K as applied to a commutative ring is the unit group construction, which was generalised to all rings for the needs of topology (simple homotopy theory) by means of elementary matrix theory. Therefore the first two cases counted as relatively accessible; while after that the theory becomes quite noticeably deeper, and certainly quite hard to compute (even when R is the ring of integers Historically the roots of the theory were in topological K-theory (based on vector bundle theory); and its motivation the conjecture of Serre that now is the Quillen-Suslin theorem . Applications of K -groups were found from 1960 onwards in surgery theory for manifolds , in particular; and numerous other connections with classical algebraic problems were found. A little later a branch of the theory for

39. :: K - T H E O R Y www.ktheory.com/ - Cachedk-theory Lunch Seminar Spring 2009A semester-long lunch seminar devoted to understanding connections between crystalline cohomology, algebraic k-theory, and topological cyclic homology. http://www.k-theory.com/

40. David Rosenthal's Home Page Cohomology of Groups and Algebraic ktheory, pp. 489501, Adv. Lect. Math. (ALM) vol. 12, Int. Press, Somerville, MA, 2010. http://facpub.stjohns.edu/~rosenthd/

David Rosenthal Contact information Address St. John's University 8000 Utopia Pkwy Jamaica, NY 11439 USA Office SJH 334C Phone Fax Email rosenthd@stjohns.edu Teaching Fall 2010 MTH 1730 "University Calculus I M 3:00-4:20 (SJH 207), TF 3:00-4:20 (SJH 314) Course home page MTH 207 "Theory of Functions of a Complex Variable" R 4:45-6:45 (SJH 211) Course home page Research Preprints K -theory and L -theory of hyperbolic and virtually finitely generated abelian groups pdf (with Published or Accepted pdf To appear in Pure and Applied Mathematics Quarterly K -theory and L -theory with twisted coefficients pdf (with Ian Hambleton and Erik K. Pedersen To appear in Pure and Applied Mathematics Quarterly pdf Cohomology of Groups and Algebraic K-theory , pp. 489501, Adv. Lect. Math. (ALM) vol. 12, Int. Press, Somerville, MA, 2010. pdf (with Andrew Nicas Proc. Amer. Math. Soc. (2009) pp. 381-38 pdf (with Andrew Nicas Algebr. Geom. Topol. (2008) pp. 693-728 K -theory of groups with finite asymptotic dimension pdf (with Arthur Bartels J. Reine Angew. Math.

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