1. K-theory - Wikipedia, The Free Encyclopedia In mathematics, ktheory is a tool used in several disciplines. In algebraic topology, it is an extraordinary cohomology theory known as topological http://en.wikipedia.org/wiki/K-theory

K-theory From Wikipedia, the free encyclopedia Jump to: navigation search To comply with Wikipedia's guidelines , the introduction of this article may need to be rewritten. Please discuss this issue on the talk page and read the layout guide to make sure the section will be inclusive of all essential details. (July 2010) In mathematics K-theory is a tool used in several disciplines. In algebraic topology , it is an extraordinary cohomology theory known as topological K-theory . In algebra and algebraic geometry , it is referred to as algebraic K-theory . It also has some applications in operator algebras . It leads to the construction of families of K functors , which contain useful but often hard-to-compute information. In physics , K-theory and in particular twisted K-theory have appeared in Type II string theory where it has been conjectured that they classify D-branes Ramond–Ramond field strengths and also certain spinors on generalized complex manifolds . For details, see also K-theory (physics) Contents Early history Developments See also Notes ... edit Early history The subject can be said to begin with Alexander Grothendieck (1957), who used it to formulate his

2. K-theory Preprint Archives Electronic preprint archives for mathematics research papers in ktheory. http://www.math.uiuc.edu/K-theory/

3. An Introduction To Algebraic K-theory An introduction to algebraic ktheory by Charles Weibel. Chapters in DVI. http://www.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

4. 19: K-theory Jan 14, 2001 Encyclopedic reference for ktheory in Dave Rusin s Mathematical Atlas. Includes a brief history along with various links to textbooks, http://www.math.niu.edu/~rusin/known-math/index/19-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 19: K-theory Introduction K-theory is an interesting blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects. History Read Atiyah's, "K-Theory Past and Present" at here Applications and related fields Most of the geometric K-theory is treated with Algebraic Topology See also 16E20, 18F25 Subfields Grothendieck groups and K_0, see also 13D15, 18F30 Whitehead groups and K_1 Steinberg groups and K_2 Higher algebraic K-theory K-theory in geometry K-theory in number theory, see also 11R70, 11S70 K-theory of forms, see also 11EXX Obstructions from topology K-theory and operator algebras See mainly 46L80, and also 46M20 Topological K-theory, see also 55N15, 55R50, 55S25 Miscellaneous applications of K-theory K-Theory is the smallest of the 61 active areas of the MSC scheme: only 515 papers with primary classification 19-XX during 1980-1997. But the area 19-XX was only available as a primary classification for Math Reviews papers starting with MR96; hence the count above is an undercount of the true size of the field. (Even granting this, however, K-theory is a fairly small field.) Browse all (old) classifications for this area at the AMS.

5. K-Theory ktheory - This journal is devoted to developments in the mathematical sciences that are related to one of the various aspects of k-theory. http://www.springer.com/mathematics/algebra/journal/10977

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6. Vector Bundles & K-Theory Book The plan is for this to be a fairly short book focusing on topological ktheory and containing also the necessary background material on vector bundles and http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html

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. Here is a provisional Table of Contents At present about half of the book is in good enough shape to be posted online, approximately 110 pages. What is included in this installment is: Chapter 1, containing basics about vector bundles. Part of Chapter 2, introducing K-theory, then proving Bott periodicity in the complex case and Adams' theorem on the Hopf invariant, with its famous applications to division algebras and parallelizability of spheres. Not yet written is the proof of Bott Periodicity in the real case, with its application to vector fields on spheres. Most of Chapter 3, constructing Stiefel-Whitney, Chern, Euler, and Pontryagin classes and establishing their basic properties. Part of Chapter 4 on the stable J-homomorphism. What is written so far is just the application of complex K-theory, using the Chern character, to give a lower bound on the order of the image of the stable J-homomorphism. Much of this material is already well covered in other sources, notably the classic books of Atiyah (

7. Cambridge Journals Online - Journal Of K-Theory ktheory and its Applications to Algebra, Geometry, Analysis and Topology Journal of k-theory is concerned with developments and applications of ideas http://journals.cambridge.org/action/displayJournal?jid=KAG

8. K-Theory And Homology Authors/titles Recent Submissions by E Angel Related articles http://arxiv.org/list/math.KT/recent

arXiv.org math math.KT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages K-Theory and Homology Authors and titles for recent submissions Fri, 29 Oct 2010 Tue, 26 Oct 2010 Mon, 25 Oct 2010 Fri, 22 Oct 2010 ... Thu, 21 Oct 2010 [ total of 9 entries: [ showing up to 25 entries per page: fewer more Fri, 29 Oct 2010 arXiv:1010.6040 pdf ps other Title: On the algebraic K-theory of formal power series Authors: Ayelet Lindenstrauss Randy McCarthy Subjects: K-Theory and Homology (math.KT) arXiv:1010.5880 pdf ps other Title: Authors: Manoj K Keshari Satya Mandal Subjects: K-Theory and Homology (math.KT) arXiv:1010.5818 pdf ps other Title: Equivariant Hopf Galois extensions and Hopf cyclic cohomology Authors: M. Hassanzadeh (UNB), B. Rangipour (UNB) Comments: 28 pages Subjects: K-Theory and Homology (math.KT) ; Quantum Algebra (math.QA) Tue, 26 Oct 2010 arXiv:1010.5002 pdf ps other Title: Talbot Workshop 2010 Talk 2: K-Theory and Index Theory Authors: Chris Kottke Comments: 16 pages Subjects: K-Theory and Homology (math.KT) ; Analysis of PDEs (math.AP)

9. Another Journal Board Resigns « Not Even Wrong Last year about this time the entire editorial board of the Elsevier journal Topology resigned, this August it’s the turn of the Springer journal ktheory. http://www.math.columbia.edu/~woit/wordpress/?p=581

10. Ingentaconnect Table Of Contents: K-Theory Share this item with others These icons link to social bookmarking sites where readers can share and discover new web pages. http://www.ingentaconnect.com/content/klu/kthe/2002/00000025/00000003

11. 2003 Honda S2000 - The K-Theory - Honda Tuning Magazine Check out this 2003 Honda S2000 with a K24A1 engine, custom flywheel, and stage IV clutch from ClutchMasters, Eagle rods, Skunk2 stage III cams, and more. Honda Tuning Magazine http://www.hondatuningmagazine.com/features/htup_1010_2003_honda_s2000/index.htm

12. SpringerLink - K-Theory, Volume 38, Number 2 www.springerlink.com/link.asp?id=100305 Similark-theory from Wolfram MathWorldOct 11, 2010 Topological K -theory is the true K -theory in the sense that it came This defines the reduced real topological K -theory of a space. http://www.springerlink.com/link.asp?id=100305

13. Milnor, J.: Introduction To Algebraic K-Theory. (AM-72). of the book Introduction to Algebraic ktheory. (AM-72) by Milnor, J., published by Princeton University Press...... http://pup.princeton.edu/titles/1568.html

14. K-Theory -- From Wolfram MathWorld A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of ktheory topological http://mathworld.wolfram.com/K-Theory.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Budney K-Theory A branch of mathematics which brings together ideas from algebraic geometry linear algebra , and number theory . In general, there are two main types of -theory: topological and algebraic. Topological -theory is the "true" -theory in the sense that it came first. Topological -theory has to do with vector bundles over topological spaces . Elements of a -theory are stable equivalence classes of vector bundles over a topological space . You can put a ring structure on the collection of stably equivalent bundles by defining addition through the Whitney sum , and multiplication through the tensor product of vector bundles . This defines "the reduced real topological -theory of a space." "The reduced -theory of a space" refers to the same construction, but instead of real vector bundles complex vector bundles are used. Topological -theory is significant because it forms a generalized cohomology theory, and it leads to a solution to the vector fields on spheres problem, as well as to an understanding of the -homeomorphism of homotopy theory Algebraic -theory is somewhat more involved. Swan (1962) noticed that there is a correspondence between the

15. :: K - T H E O R Y After a 10 year stint in Denver, Colorado, I've recently relocated to the San contact@ktheory.com http://k-theory.com/

16. SEMI-TOPOLOGICALK-THEORY OF REAL VARIETIES SEMITOPOLOGICALk-theory OF REAL VARIETIES EricM. Friedlanderand Mark E. Walker Abstract. The semi-topological k-theory of real varieties, KR semi (), is an oriented http://www.math.unl.edu/~mwalker5/papers/KRsemi.pdf

17. Algebraic K-Theory In AvaxHome V. Srinivas, Algebraic ktheory Birkh user Boston 2007 ISBN 0817647368 342 pages PDF 13,9 MB http://avaxhome.ws/ebooks/science_books/math/0817647368kTheory.html

var VerifyCode = "881ba11f7ff8262"; Loading... Done Play OnLine Games Download Games Home Music ... Science ABUSE FORM Short Reason: Algebraic K-Theory Posted By : Date : Comments : V. Srinivas, "Algebraic K-Theory" Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. This new edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience. A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers “Higher Algebraic K-Theory, I, II.” A more elementary proof of the theorem of MerkujevSuslin is given in this edition; this makes the treatment of this topic self-contained. An applications is also given to modules of finite length and finite projective dimension over the local ring of a normal surface singularity. These results lead the reader to some interesting conclusions regarding the Chow group of varieties. Download uploading.com

18. Algebraic K-theory - Wikipedia, The Free Encyclopedia In mathematics, algebraic ktheory is an important part of homological algebra concerned with defining and applying a sequence. of functors from rings to abelian groups, for http://en.wikipedia.org/wiki/Algebraic_K-theory

Algebraic K-theory From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics algebraic K-theory is an important part of homological algebra concerned with defining and applying a sequence K n R of functors from rings to abelian groups , for all integers n. For historical reasons, the lower K-groups K and K are thought of in somewhat different terms from the higher algebraic K-groups K n for n ≥ 2. Indeed, the lower groups are more accessible, and have more applications, than the higher groups. The theory of the higher K-groups is noticeably deeper, and certainly much harder to compute (even when R is the ring of integers The group K R ) generalises the construction of the ideal class group of a ring, using projective modules . Its development in the 1960s and 1970s was linked to attempts to solve a conjecture of Serre on projective modules that now is the Quillen-Suslin theorem ; numerous other connections with classical algebraic problems were found in this era. Similarly, K R ) is a modification of the group of units in a ring, using

19. Elliptic Cohomology And 2-K-theory Of 2-vector Spaces About this document Elliptic cohomology and 2k-theory of 2-vector spaces. John Rognes. Generalized cohomology theories are filtered by how much of the stable homotopy theory of http://www.maths.abdn.ac.uk/~stc2001/abstracts/Rognes/Rognes.html

Next: About this document ... Elliptic cohomology and 2- K -theory of 2-vector spaces John Rognes Generalized cohomology theories are filtered by how much of the stable homotopy theory of finite CW -complexes they detect: rational cohomology has filtration 0, topological K-theory has filtration 1, Morava's theory K n ) has filtration n, and complex cobordism has filtration infinity. This is a version of the chromatic filtration. Some of these theories admit concrete constructions, in terms of differential forms, vector bundles or manifolds. This is desirable, because e.g. the curvature of a connection, or the kernel of an family of operators may naturally give rise to such objects, and thus to elements in the cohomology theory. Baas-Dundas-Rognes study a kind of 2- K -theory of the 2-category of 2-vector spaces considered by Kapranov-Voevodsky. The represented cohomology theory carries invariants of certain stacks (sheaves of categories) that include gerbes as a special case. This 2- K -theory can also be interpreted as the algebraic K -theory of topological K -theory, viewed as a `brave new ring' or

20. Dr. Xianzhe Dai (Math, UCSB), Introduction To K-Theory Schedule Apr 7, 2000 Introduction to ktheory Dr. Xianzhe Dai (Math, UCSB) This is an introduction to vector bundles and their classification. Audio for this talk requires sound http://online.itp.ucsb.edu/online/ktheory/dai/

Schedule Apr 7, 2000 Introduction to K-Theory Dr. Xianzhe Dai (Math, UCSB) This is an introduction to vector bundles and their classification. Audio for this talk requires sound hardware, and RealPlayer or RealAudio by RealNetworks. Begin continuous audio for the whole talk . (Or, right-click to download the whole audio file To begin viewing slides, click on the first slide below. Author entry (protected)

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