61. DC MetaData For:K-theory And Generalized Free Products Of S-algebras: Localizati ktheory and generalized free products of S-algebras Localization methods.Roland MSC 2000 19D10 Algebraic $K$-theory of spaces. Abstract http://www.mathematik.uni-osnabrueck.de/preprints/shadow/dsm99XXX.rdf.html

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) are satisfied for two fundamental notions of weak equivalence, and there is, therefore, a three-term fibration sequence up to homotopy in which the K-theory of Mayer-Vietoris presentations with respect to the fine notion of equivalence is compared with the K-theory with respect to the coarse notion. The rest of the paper is concerned with interpreting these K-theories in terms of the K-theories of the algebras in the generalized free product diagram.

62. Algebraic K-Theory ALGEBRAIC ktheory SEMINARS. Last Updated 06/02/02. . Mon, Tue, Wed,Thu, Fri. 08.00-10.00, . . . . . 10.00-12.00, . . . . 12.00-14.00, . .. . http://www.math.uio.no/OMATS/kt/seminars/seminars.htm

SEMINARS Last Updated: Mon Tue Wed Thu Fri Elliptic Curves and Cryptology Algebraic Geometry Topology Operator algebras Non-commutative geometry

63. K-theory The slides for my talk in Metz. Preprint Boundsfor computing the tame kernel , report 200213. http://www.math.leidenuniv.nl/~groen/ktheory.html

The slides for my talk in Metz Preprint: "Bounds for computing the tame kernel", report 2002-13

64. Stable Differential Forms ktheory. Professor CB Thomas and Professor B Totaro k-theory is aricher cohomology theory than ordinary cohomology and so provides http://www.maths.cam.ac.uk/CASM/essays/absextra/node5.html

Next: Arithmetic Structure in Difference Up: Faculty of Mathematics Extra Previous: Crystals and the Weyl Stable Differential Forms Dr A G Kovalev The term `stable form' was suggested by Hitchin for an alternating form having an open orbit in the natural action of GL n ). Stable forms generalize the notion of non-degenerate bilinear forms to alternating forms of any degree p and non-trivial examples include stable forms of degree p =3 in dimensions n =6 and 7. The essay could begin by exploring the work [1] and showing how stable differential 3-forms lead to Ricci-flat metrics on 6- and 7-dimensional manifolds, via the holonomy reduction [2]. In dimension 6 this gives an alternative view on Calabi-Yau complex 3-folds and in dimension 7 a special geometry defined by the structure group G . The essay may investigate the significance of stable forms in either of these two geometries. There is also an option to discuss the interplays with the theory of calibrated minimal submanifolds [3]. References [1] N. Hitchin, The geometry of three-forms in six and seven dimensions , arXiv:math.DG/0010054.

65. K-theory Operations Prifysgol Cymru Abertawe/University of Wales Swansea, ktheory operations. section1.paris, The Algebra of Operations in k-theory (Paris, January 2002). Top. http://www-maths.swan.ac.uk/staff/fwc/HAOCKT.html

K-theory operations University Mathematics Francis Clarke Research Interests ... Text Paris version Swansea version paris The Algebra of Operations in K-theory (Paris, January 2002) K th January 2002. The slides themselves (dvi file) The slides as a text document (dvi file) The source for these two files (tex file, including two other files) A historical introduction (dvi file) Its source (tex file, needs files included above) swansea The Algebra of Operations in K-theory (Wales, October 2002) Also available is the text of a University of Wales video seminar given on 17 th K The text of the seminar (dvi file) The text of the seminar (pdf file) The source (tex file, including two other files) University Mathematics Francis Clarke Research Interests 21 January 2003 Webmaster

66. An Introduction To K-theory An Introduction to ktheory. An Introduction to k-theory. An Introductionto k-theory, Top. You will find here the text of 2 http://www-maths.swan.ac.uk/staff/fwc/IKTt.html

PRIFYSGOL CYMRU ABERAWE, UNIVERSITY OF WALES SWANSEA. University Mathematics Francis Clarke Research Interests ... Graphics. An Introduction to K-theory An Introduction to K -theory An Introduction to K-theory Top K th Transpenine Topology Triangle th The text of the lectures (pdf file) The text of the lectures (dvi file) The dvi version needs graphics file 1 (ps file) and graphics file 2 for printing or viewing (ps file) University Mathematics Francis Clarke Research Interests ... Graphics. 21 January 2003 Webmaster

67. Michael Atiyah; Twisted K-theory And Physics Michael Atiyah. Twisted ktheory and physics . audio start (ogg vorbis),start (realaudio). download (ogg vorbis), download (realaudio). http://www.damtp.cam.ac.uk/strings02/avt/atiyah/

Contact: strings2002@damtp.cam.ac.uk Pre-arrival: Registration Accommodation Getting to Cambridge Conference: Post-arrival information Conference information Schedule of talks Speakers and titles ... Social events Other: Organisation Other Strings Conferences Sponsors Conference Home ... DIRAC CENTENNIAL Michael Atiyah "Twisted K-theory and physics" audio: start (ogg vorbis) start (realaudio) download (ogg vorbis) download (realaudio) video: start (realplayer, 460Kbps bandwidth) download (realplayer) transparencies: download all transparencies (postscript) download all transparencies (postscript, 4 slides on one page)

68. Topics In K-theory And L-functions Topics in ktheory and L-functions. The course meets Tuesdays and Thursdays1130 - 100 in Science Center 310. Fernando Rodriguez Villegas. http://www.math.harvard.edu/~villegas/course.html

69. ON THE K-THEORY OF C*-ALGEBRAS OF PRINCIPAL GROUPOIDS ON THE ktheory OF C * -ALGEBRAS OF PRINCIPAL GROUPOIDS. IAN F. PUTNAM. AbstractWe consider the k-theory of C * -algebras of principal r-discrete groupoids. http://math.la.asu.edu/~rmmc/rmj/VOL28-4/PUT/PUT.html

ON THE K -THEORY OF C -ALGEBRAS OF PRINCIPAL GROUPOIDS IAN F. PUTNAM Abstract: We consider the K -theory of C -algebras of principal r -discrete groupoids. We describe two basic situations in which three groupoids are related; they can very loosely be described as ``factor groupoids'' and ``subgroupoids.'' For each, we show that there is a six-term exact sequence of associated K -groups. We present examples which arise from dynamical systems and from problems in the study of the orbit structure of topological systems. We also obtain the usual Mayer-Vietoris sequence in topological K -theory as a corollary.

70. D-branes, B-fields And Twisted K-theory My papers on Dbranes in the presence of B-fields, and twisted k-theoryThe theory of D-branes forms part of string theory. Open http://www.maths.adelaide.edu.au/Pure/vmathai/dbrane.html

My papers on D-branes in the presence of B-fields, and twisted K-theory The theory of D-branes forms part of string theory. Open strings that are endowed with Dirichlet boundary conditions so that the endpoint is fixed to move only on some manifold - this manifold is called 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 (M, Z ), Witten argued that D-branes no longer carry honest vector bundles, but they have a twisted or gauge bundle. In the presence of a nontrivial B-field whose Dixmier-Douady class is a general element of H (M, Z ), it was proposed in [BM] that D-brane charges in type IIB string theories are measured by the twisted K-theory that was described earlier by Rosenberg, and the twisted bundles on the D-brane world-volumes were elements in this twisted K-theory. In [BCMMS] , using bundle gerbes and their modules, a geometric interpretation of elements of twisted K-theory was obtained, and the the Chern-Weil representatives of the Chern character was studied. This was further generalized to the equivariant and the holomorphic cases in

71. K-theory Preprint Archives ktheory Preprint Archives. http//www.math.uiuc.edu/k-theory/. FeaturesWeb Journal , , - This is a preprint archive in .dvi format. http://www.aldea.com/guides/ag/a813ud.html

K-theory Preprint Archives http://www.math.uiuc.edu/K-theory/ Features: Web Journal , , . Community Commentary Faculty: Quality ; Quantity ; Ease ; Up-to-date Graduates: Quality ; Quantity ; Ease ; Up-to-date Undergraduates: Quality ; Quantity ; Ease ; Up-to-date Other: Quality ; Quantity ; Ease ; Up-to-date Back to Mathematical sciences Community Commentary Back to UniGuide Academic Guide Site developed and designed by AldeaCommunications For inquiries or to make suggestions email uniguide@aldea.com Last Modified: 8/14/97

72. Twisted K-theory And K-theory Of Bundle Gerbes Twisted ktheory and k-theory of bundle gerbes P. Bouwknegt, AL Carey,V. Mathai, MK Murray and D. Stevenson ADP-01-29/M98, hep-th/0106194. http://www.physics.adelaide.edu.au/mathphysics/abstracts/ADP-01-29-M98.html

Twisted K-theory and K-theory of bundle gerbes P. Bouwknegt, A.L. Carey, V. Mathai, M.K. Murray and D. Stevenson ADP-01-29/M98, hep-th/0106194. In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed. Link to Los Alamos archive: in [ Australia ]; in [ United States SLAC Citation search HOME

73. Penn State Workshop On Uniformly Bounded Representations And K- Workshop on Uniformly Bounded Representations and ktheory. October22-27 1999. The main purpose of this small workshop is to explore http://www.math.psu.edu/gfa/PastMeetings/ubworkshop.html

74. Penn State Workshop On Uniformly Bounded Representations And K- Workshop on Uniformly Bounded Representations and ktheory. October22-27 1999. Schedule. The main purpose of this small workshop is http://www.math.psu.edu/gfa/PastMeetings/ubschedule.html

75. Programme K-Theory k-theory L-groups. Research in k-theoryin Nijmegen has been done since the early 70's. To the Homepage.......Programme ktheory. http://www-math.sci.kun.nl/onderzoek/prog_algebra2.html

Programme K-Theory Description K-theory has its roots in both algebraic geometry (Grothendieck's proof in 1958 of a general type of Riemann-Roch theorem) and algebraic topology (Whitehead torsion of manifolds, also in the 50's). Later, around 1970, algebraic topology was used for the construction of higher K-groups by Quillen, Swan, Gersten, Volodin and Keune. At the same time it became clear that there were many relations with classical subjects in number theory and geometry. For instance, the K2 of a number field turned out to be very closely connected to class field theory. The study of surgery on manifolds led to the introduction of new algebraic invariants, the L-groups. Research in K-theory in Nijmegen has been done since the early 70's. To the Homepage.

76. Algebraic K-theory . Identifier K alg (MathML mathmlxmlns= http//www.w3.org/1998/Math/MathML ci msup mi K /mi......Algebraic ktheory. http://www.maths.qmul.ac.uk/~mh/categories/algebraic_k-theory.html

Algebraic K-theory Description Identifier : K alg (MathML: From Rings To Abelian groups Properties Natural transformations Back to index

77. Topological K-theory Topological ktheory. 120pt 4 hours of lectures per week. Lecturer Univ.1989, and k-theory, Lecture Notes Series 11, Aarhus Univ. 1968. http://www.imf.au.dk/Mathematics/education/E99/courses2/node59.html

Next: C courses - advanced Up: C courses - introductory Previous: Spectral theory of Laplacians Topological K -theory 4 hours of lectures per week. Lecturer: Johan Dupont Content: Similarly to the cohomology theory developed in Topology 1 one constructs in topological K -theory to each topological space X an associated Abelian group K X ). This is a rather strong invariant for the topological space and when it was introduced in the 60-s it immediately solved some rather difficult geometric problems. At the same it was the basic tool in the study of topological properties of elliptic differential equations (index theory) and thus became the starting point of a successful interplay between topology and analysis. Today the notion of K -theory occurs in many different areas of mathematics: Index theory in differential geometry and global analysis, Algebraic K -theory in algebra and algebraic topology, and KK -theory in operator algebra, just to mention a few. In the course we shall begin with the elementary notions from general topology and proceed with the basic properties of vector bundles leading to the construction of topological K -theory and some of its classical applications.

78. K - THEORY Translate this page K -. K – THEORY. k-theory. Dordrecht,Netherlands Kluwer Academic Publishers,1987-. ISSN 0920-3036. Frecuencia de publicación anterior 1 vol. http://www.matem.unam.mx/servicios/biblioteca/2001/k/ka.html

Inicio Servicios Biblioteca K A B C D ... J K L M N O ... Z - K - K-Theory Dordrecht,Netherlands : Kluwer Academic Publishers, 1987- ISSN 0920-3036 Web: http://www.wkap.nl/journalhome.htm/0920-3036

79. Semi-topological K-theory Of Real Varieties Semitopological k-theory of Real Varieties. By Eric M. Friedlanderand Mark E. Walker. This paper is available in the following http://www.math.nwu.edu/~eric/preprints/real/

Semi-topological K-theory of Real Varieties By: Eric M. Friedlander and Mark E. Walker This paper is available in the following formats: TeX Source file DVI file

80. Atlas: Profinite And Continuous Higher K-Theory Of Exact Categories, Schemes, Or Conference Homepage. Profinite and continuous Higher ktheory ofExact categories, schemes, Orders and Group-rings. presented by http://atlas-conferences.com/c/a/g/f/13.htm

Atlas Document # cagf-13 Nordic Conference on Topology and its Applications (NORDTOP2001) August 7-9, 2001 Sophus Lie Conference Centre Nordfjordeid, Norway Conference Organizers Peter Collins, Bjoern Jahren, Dusan Repovs and Stephen Watson View Abstracts Conference Homepage Profinite and continuous Higher K-Theory of Exact categories, schemes, Orders and Group-rings. presented by Aderemi Kuku International Centre for Theoretical physics, Trieste, Italy. Let C be an exact category. In this lecture, we define and study the profinite Higher K-theory and some other associated K-theories of C and prove several l-completeness results in the general setting of exact categories. We then specialise C to the category P(X) of locally free sheaves of O X modules (X a scheme) and C = P(A) the category of finitely generated projective modules over any ring A (not necessarily commutative) with identity as well as the category C = M(x) of coherent sheaves of O X modules (X a Noetherian Schemme) and the category M(A) of finitely generated modules over a (not necessarily commutative) Noetherian ring A. For computational purposes, we specialise further to the categories P(A) and M(A) where the A are orders in semisimple algebras over number fields and p-adic fields. We also define and study continuous Higher K-theory of orders A in p-adic semisimple algebras and show some connection between the profinite and continuous K-theory of A. Date received: June 18, 2001

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