61. Title Details - Cambridge University Press Home Catalogue An Introduction to ktheory for C*-Algebras. Related Areas An Introduction to k-theory for C*-Algebras. M. Rørdam, F. Larsen, N. Laustsen. http://titles.cambridge.org/catalogue.asp?isbn=0521789443

62. K-THEORY AND NONCOMMUTATIVE GEOMETRY ktheory AND NONCOMMUTATIVE GEOMETRY. March 1, 2004-July 17, 2004. Second announcement Planning. Institut Henri Poincaré, Centre Emile http://www.ihp.jussieu.fr/ceb/ceb-progscient-encours.html

K-THEORY AND NONCOMMUTATIVE GEOMETRY March 1, 2004-July 17, 2004 Second announcement Planning Institut Henri Poincaré, Centre Emile Borel 11, rue Pierre et Marie Curie, Paris 05, France Tél. (33) 1 44 27 67 64 Fax (33) 1 44 07 09 37 It is highly recommended to register on the IHP Web site : www.ihp.jussieu.fr Organizers : Max KAROUBI, Ryszard NEST This Semester in the Centre Emile Borel will present the state of the art in Noncommutative Geometry and Algebraic K-theory, as well as the interrelation between the two subjects. Long courses Alain CONNES Course in the Collège de France (formes modulaires et géométrie non commutative) Fabien MOREL Introduction to motivic homotopy theory of schemes Boris TSYGAN Cyclic homology, noncommutative differential calculus and index theorems Short courses Eric M. FRIEDLANDER Cohomology and K-theory web Lars HESSELHOLT The de Rham-Witt complex and topological Hochschild homology Vincent LAFFORGUE KK-theory and applications Ryszard NEST Deformation quantization and index theorems Victor NISTOR K-theory and cyclic homology web Dimitri TAMARKIN Operads and formality theorems Series of lectures on advanced subjects Paul BAUM Jean BELLISSARD Joachim CUNTZ,

63. Topics In K-theory And L-functions Topics in ktheory and L-functions. The course meets Tuesdays and Thursdays 1130 - 100 in Science Center 310. Fernando Rodriguez Villegas. http://www.math.harvard.edu/~villegas/course.html

Topics in K-theory and L-functions The course meets Tuesdays and Thursdays 11:30 - 1:00 in Science Center 310. Fernando Rodriguez Villegas Department of Mathematics Harvard University Science Center 430 villegas@math.harvard.edu Office Hours Tues, Thurs 10:00 - 11:00 Suggested exercises on periods. Notes last updated: May 14, 2002. The following are class notes taken by Sam Vandervelde (samv@mandelbrot.org). Please let me or Sam know of any comments, corrections, etc. Thanks. Notes 1 Notes 2 Notes 3 Notes 4 ... Notes 5 The following are class notes taken by Matilde Lalin (mlalin@math.harvard.edu). Please let me or Matilde know of any comments, corrections, etc. Thanks. Notes 6

64. Milnor, J.W.: Introduction To Algebraic K-Theory. (AM-72). Introduction to Algebraic ktheory. (AM-72). John Willard Milnor. Paper 1972 $35.00 / £22.95 ISBN 0-691-08101-8 200 pp. Shopping Cart. http://pup.princeton.edu/titles/1568.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Introduction to Algebraic K-Theory. (AM-72) John Willard Milnor 200 pp. Shopping Cart Other Princeton books by John Willard Milnor: Characteristic Classes. (AM-76). Morse Theory. (AM-51). Prospects in Mathematics. (AM-70). Singular Points of Complex Hypersurfaces. (AM-61). ... Topology from the Differentiable Viewpoint. Series: Annals of Mathematics Studies Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors Subject Area: Mathematics VISIT OUR MATH WEBSITE Paper: Not for sale in Japan Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia Paper: $35.00 ISBN: 0-691-08101-8 For customers in Europe, Africa, the Middle East, and India Prices subject to change without notice File created: 5/7/04 Questions and comments to: webmaster@pupress.princeton.edu Princeton University Press

65. Bak, A.: K-Theory Of Forms. (AM-98). ktheory of Forms. (AM-98). Anthony Bak. Paper 1981 $37.50 / £24.95 ISBN 0-691-08275-8 280 pp. Shopping Cart. Series Annals http://pup.princeton.edu/titles/70.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE K-Theory of Forms. (AM-98) Anthony Bak 280 pp. Shopping Cart Series: Annals of Mathematics Studies Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors Subject Area: Mathematics VISIT OUR MATH WEBSITE Paper: Not for sale in Japan Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia Paper: $37.50 ISBN: 0-691-08275-8 For customers in Europe, Africa, the Middle East, and India Prices subject to change without notice File created: 5/7/04 Questions and comments to: webmaster@pupress.princeton.edu Princeton University Press

66. Encyclopedia4U - K-theory - Encyclopedia Article ktheory. In turn, Jean-Pierre Serre used the analogy of vector bundles with projective modules to found in 1959 what became algebraic k-theory. http://www.encyclopedia4u.com/k/k-theory.html

ENCYCLOPEDIA U com Lists of articles by category ... Encyclopedia Home Page SEARCH : 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.

67. K-theory Definition Meaning Information Explanation ktheory. In turn, Jean-Pierre Serre used the analogy of vector bundles with projective modules to found in 1959 what became algebraic k-theory. http://www.free-definition.com/K-theory.html

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term 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- functor s, 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 bundle s. 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 bundle s with projective module s to found in 1959 what became algebraic K-theory . He made Serre's conjecture , that projective modules over the ring of polynomial s over a field are free module s; this resisted proof for 20 years.

68. PlanetMath: K-theory This is version 14 of ktheory, born on 2002-08-23, modified 2004-04-16. Object id is 3338, canonical name is KTheory. Accessed 1500 times total. http://planetmath.org/encyclopedia/KTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List K-theory (Topic) Topological K-theory is a generalised cohomology theory on the category of compact Hausdorff spaces. It classifies the vector bundles over a space up to stable equivalences . Equivalently, via the Serre-Swan theorem , it classifies the finitely generated projective modules over the -algebra Let be a unital -algebra over and denote by the algebraic direct limit of matrix algebras under the embeddings . Identify the completion of with the stable algebra (where is the compact operators on ), which we will continue to denote by . The group is the Grothendieck group abelian group of formal differences ) of the homotopy classes of the projections in . Two projections and are homotopic if there exists a norm continuous path of projections from to . Let and be two projections. The sum of their homotopy classes

69. PlanetMath: K-theory This is version 14 of ktheory, born on 2002-08-23, modified 2004-04-16. Object id is 3338, canonical name is KTheory. Accessed 1510 times total. http://planetmath.org/encyclopedia/TopologicalKTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List K-theory (Topic) Topological K-theory is a generalised cohomology theory on the category of compact Hausdorff spaces. It classifies the vector bundles over a space up to stable equivalences . Equivalently, via the Serre-Swan theorem , it classifies the finitely generated projective modules over the -algebra Let be a unital -algebra over and denote by the algebraic direct limit of matrix algebras under the embeddings . Identify the completion of with the stable algebra (where is the compact operators on ), which we will continue to denote by . The group is the Grothendieck group abelian group of formal differences ) of the homotopy classes of the projections in . Two projections and are homotopic if there exists a norm continuous path of projections from to . Let and be two projections. The sum of their homotopy classes

70. C*-algebras And K-theory 2003-04 C*algebras and k-theory 2003-04. Lecture Notes. Part II k-theory for C*-algebras Overview of k-theory; Projections in C*-algebras; http://remote.science.uva.nl/~npl/CK.html

C*-algebras and K-theory 2003-04 Lecture Notes Part I: [pdf] [ps] Part II: [pdf] [ps] Exercises Part I: [pdf] [ps] (exam included) Part II: [pdf] [ps] Take-home exam for Part II Give a complete proof of Cuntz' theorem: Any functor E from the category of C*-algebras to the category of abelian groups that is i) stable; ii) half-exact; iii) homotopy invariant, satisfies Bott periodicity (where the higher E-groups are defined via suspension, as for E=K). Literature: J. Cuntz, K-theory and C*-algebras, Lecture Notes in Mathematics 1046 (1984) 55-79 N.E. Wegge-Olsen, K-Theory and C*-Algebras (Oxford, 1993) N. Higson and J. Roe, Analytic K-Homology (Oxford, 2000). Answers to the take-home exam (Part I) [pdf] [ps] Preliminary answers to the exercises (unauthorized!) Part I: [pdf] [ps] Part II: [pdf] [ps] Lecturer: prof.dr. N.P. Landsman npl@science.uva.nl Exercise class: dr. C. Carvalho ccarvalh@science.uva.nl Audience: MRI Masterclass students, M.Sc. students in mathematics or theoretical physics. Prerequisites: Elementary topology and differential geometry, basic theory of Hilbert and Banach spaces (definitions, basic theorems, and simple examples). Mathematics students should have acquired this background in Analysis 1B, 2A, Real analysis, and Differental geometry. Theoretical physics students should know this material from Quantum Mechanics, Geometric Methods in Physcs, and general education.

71. Twisted K-theory And Strings My papers on twisted ktheory, strings and duality The isomophisms in twisted k-theory and twisted cohomology also follow in this case. http://www.maths.adelaide.edu.au/people/vmathai/dbrane.html

My papers on twisted K-theory, strings and duality String theory is arguably the most exciting research area in modern mathematical physics. It is known to the general public as the "Theory Of Everything", thanks to its great success in unifying Relativity and Quantum Field Theory, yielding Quantum Gravity theory. The impact of string theory is not just felt in physics, but it also has profound interactions with a broad spectrum of modern mathematics, including noncommutative geometry, K-theory and index theory. The pioneers of string theory were M.B. Green and J.H. Schwarz and the leading figure in the field is E. Witten The theory of D-branes forms an important part of string theory. It arises as the T-dual of open strings on a circle bundle, where the open strings in the dual theory are no longer free to move everywhere in space, but are endowed with Dirichlet boundary conditions so that the endpoints are free to move only on a submanifold known as a D-brane. For a link describing the mathematics behind D-branes, cf. superstrings . Such D-branes come with (Chan-Paton) vector bundles, and therefore their charge determines an element of K-theory, as was argued by Minasian-Moore. In the presence of a nontrivial B-field but whose Dixmier-Douady class is a torsion element of H

72. K-theory And Analysis Durham Symposium. ktheory and analysis. The Durham Symposium on k-theory and analysis took place from 6 to 13 July 2000, with lectures running 7 - 12 July. http://www.mcs.le.ac.uk/~jhunton/KTA.html

Durham Symposium K-theory and analysis 6 - 13 July 2000 The Durham Symposium on K-theory and analysis took place from 6 to 13 July 2000, with lectures running 7 - 12 July. The symposium was centred around the theme of K-theory for group C*-algebras and involved the interaction of K-theory with geometry. The overarching idea was that K-theory groups should be seen as a way of organizing certain kinds of geometric structures 'up to deformation'. The symposium represented applications of K-theory that touch upon many different areas of mathematics and drew together a wealth of mathematical ideas. The programme included K-theory for group algebras, the Novikov conjecture, cyclic homology, and dynamical systems all of which have a link to the Baum-Connes conjecture; the K-theory involved ran all the way through its topological, analytic and algebraic versions. The theme, which is developing extremely rapidly at the present time, brought together experts representing mathematical disciplines that are unified in unexpected ways by a few deep and difficult problems. A number of important and new results were announced at the conference, e.g. a proof of the Baum-Connes conjecture for adelic groups. There was also a number of expository talks aimed at postgraduate students. The small size of the Symposium allowed for a lot of informal discussion and interaction between the areas represented.

73. Fiche Document -Algebraic K-theory Translate this page Ouvrage - Cote 00014501 - (disponible) Algebraic k-theory Suslin, AA (Editeur) Providence RI American mathematical society 1991 faiseaux de fibres k http://bibli.cirm.univ-mrs.fr/Document.htm&numrec=031997068917980

74. Fiche Document -The Classical Groups And K-theory http://bibli.cirm.univ-mrs.fr/Document.htm&numrec=031982535916430

75. What Is K-Theory What Is ktheory? k-theory is a branch of general linear algebra. Roughly speaking, k-theory is the study of additive (or abelian http://www.math.usf.edu/~emohamed/K_THEORY.htm

What Is K -Theory? K -theory is a branch of general linear algebra. Roughly speaking, K -theory is the study of additive (or abelian) invariants of matrices over a ring R Here are some "basic" examples: Whether or not the rank of a free R -module is an invariant depends on the ground ring R [There are examples of rings which do not satisfy the invariant basis property (IBP): R m and R n are not isomorphic for m n Multiplication of matrices is not commutative; however, given "enough room" by identifying A with and B with , we obtain ( A basic theorem of linear algebra states that: dim (ker f ) + dim (Im f = n, where f is a morphism of K -vector spaces f K n K m An attempt to understand how this theorem may be generalized to arbitrary rings generated the notion of projective module (direct summand of free module). K -theory associates to any ring R a sequence of abelian groups K i R The Grothendieck group K o (R ) (introduced in the sixties), while formulating and proving the Riemann-Roch theorem for algebraic vector bundles, is defined by a process of analogous to the formation of the integers from the natural numbers or of the localization of a ring with respect to a multiplicative set, like the construction of rationals from to integers. This process is called group completion.

76. TUD : Vorlesungen Sommersemester 04 - TUD: Kommentar Zu: K-Theory Translate this page TUD Kommentar zu k-theory. zum Seitenende. Nr. k-theory, V2, Fr, 9.50-11.30, S207/109, 16.04. Kramer, 3,0, 04.125.1. Inhalt (kurze Beschreibung) http://www.tu-darmstadt.de/vv/comments/04.125.tud

Vorlesungen Sommersemester 04 TUD: Kommentar zu: K-Theory Lehrveranstaltungen des Fachbereichs Kommentar zur Lehrveranstaltung: Veranstaltung Typ Tag Zeit Raum Beginn Dozent/in CPs Lv. Nr. K-Theory Fr Kramer Inhalt (kurze Beschreibung): Die topologische K-Theorie ist eine von Atiyah und Hirzebruch entwickelte sogenannte Kohomologietheorie. Die grundlegende Idee ist, einem topologischen Raum eine algebraische Struktur - einen Ring K(X) - zuzuordnen und aus der Ringstruktur Rückschlüsse über die Topologie zu gewinnen. Eines der Ziele der Volesung wird der Beweis von Adams' wichtigem Satz über stetige Multiplikationen auf Sphären und euklidischen Räumen sein. Voraussetzungen zur Teilnahme: An Vorkenntnissen werden benötigt: Lineare Algebra (reelle und komplexe Vektorräume und die linearen Gruppen) und Grundkenntnisse in (mengentheoretischer) Topologie. Ich werde mich an den Vorkenntnissen der Hörer orientieren. Angebotsturnus: unregelmäßig Vorlesungssprache: Deutsch Kramer

77. EEVL | Mathematics Section | Browse Mathematics Algebra ktheory spey 1 vaich 1 This browse section has 8 records spey 1 vaich 1 3. k-theory and Homology Front for the Mathematics ArXiv. http://www.eevl.ac.uk/mathematics/math-browse-page.htm?action=Class Browse&brows

78. FIM - Algebraic Cycles And Algebraic K-Theory Algebraic Cycles and Algebraic ktheory. Eric M. Friedlander, Northwestern University Beginning Thursday, October 30, 2003 Time Wednesday http://www.fim.math.ethz.ch/activities/eth_lectures/archive/ws0304/friedlander

Contact Guests Information for Guests Contact ... WS 99/00 Algebraic Cycles and Algebraic K-Theory Eric M. Friedlander , Northwestern University Beginning: Thursday, October 30, 2003 Time: Wednesday 10:00-12:00 Room: HG G 43 (Hermann-Weyl-Zimmer) Abstract Imprint

79. DC MetaData For:K-theory And Generalized Free Products Of S-algebras: Localizati Bielefeld ktheory and generalized free products of S-algebras Localization methods. MSC 2000 19D10 Algebraic $K$-theory of spaces. Abstract http://www.iwi-iuk.org/material/RDF/1.1/profile/MNPreprint/ex2.rdf.html

Stable K-theory, Topological Hochschild Homology, Generalized free products, S-Algebras, Localization K-theory and generalized free products of S-Algebras: Localization methods Roland Ross E. Staffeldt Staffeldt Ross E. Friedhelm Waldhausen Waldhausen Friedhelm Diskrete Strukturen in der Mathematik, P 99, SFB 343 Bielefeld" K-theory and generalized free products of S-algebras: Localization methods Ross E. Staffeldt Friedhelm Waldhausen Preprint series: Diskrete Strukturen in der Mathematik, P 99, SFB 343 Bielefeld MSC 2000 19D10 Algebraic $K$-theory of spaces Abstract A generalized free product diagram of S-algebras is a generalization and stabilization of the diagram of group rings arising from a Seifert-van Kampen situation. Our eventual goal is to obtain a description of the algebraic K-theory of the ``large'' algebra in a generalized free product diagram in terms of the K-theories of the three smaller algebras. We first provide foundational material on generalized free product diagrams of S-algebras and associated categories of Mayer-Vietoris presentations. We show that the categories of Mayer-Vietoris presentations are categories with cofibrations, weak equivalences, and mapping cylinders. In particular, the hypotheses of the ``generic fibration theorem'' of Waldhausen ( Algebraic K-theory of spaces, Lecture Notes in Math. 1126(1985), 318-419)

80. A Pieri-Chevalley Formula In The K-theory Of A G/B-bundle The master copy is available at http//www.ams.org/era/. A PieriChevalley formula in the k-theory of aG/B-bundle. Harsh Pittie and Arun Ram. Abstract. http://www.mpim-bonn.mpg.de/external-documentation/era-mirror/1999-01-014/1999-0

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ A Pieri-Chevalley formula in the K-theory of a G/B-bundle Harsh Pittie and Arun Ram Abstract. Retrieve entire article TeX source DVI PostScript Article Info ERA Amer. Math. Soc. (1999), pp. 102-107 Publisher Identifier: S 1079-6762(99)00067-0 Mathematics Subject Classification . Primary 14M15; Secondary 14C35, 19E08 Key words and phrases Received by the editors February 9, 1999 Posted on July 14, 1999 Communicated by Efim Zelmanov Comments (When Available) Harsh Pittie Department of Mathematics, Graduate Center, City University of New York, New York, NY 10036 Arun Ram Department of Mathematics, Princeton University, Princeton, NJ 08544 E-mail address: rama@math.princeton.edu Research supported in part by National Science Foundation grant DMS-9622985. Electronic Research Announcements of the AMS Home page

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