LEADER 04361nam 2200625 450 001 9910146559803321 005 20210209125742.0 010 $a3-540-74956-X 024 7 $a10.1007/978-3-540-74956-1 035 $a(CKB)1000000000492145 035 $a(SSID)ssj0000316438 035 $a(PQKBManifestationID)11247262 035 $a(PQKBTitleCode)TC0000316438 035 $a(PQKBWorkID)10281804 035 $a(PQKB)11089270 035 $a(DE-He213)978-3-540-74956-1 035 $a(MiAaPQ)EBC3062072 035 $a(MiAaPQ)EBC6350776 035 $z(PPN)25884583X 035 $a(PPN)123739764 035 $a(EXLCZ)991000000000492145 100 $a20210209d2008 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBasic bundle theory and k-cohomology invariants /$fDale Husemo?ller, Michael Joachim, Branislav Jurco, Martin Schottenloher, S. Echterhoff, B. Kro?tz, Dale Husemo?ller, B. Kro?tz 205 $a1st ed. 2008. 210 1$aBerlin, Germany ;$aNew York, United States :$cSpringer,$d[2008] 210 4$dİ2008 215 $a1 online resource (XV, 340 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v726 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-74955-1 320 $aIncludes bibliographical references (pages [323]-325) and indexes. 327 $aPhysical Background to the K-Theory Classification of D-Branes: Introduction and References -- Physical Background to the K-Theory Classification of D-Branes: Introduction and References -- Bundles over a Space and Modules over an Algebra -- Generalities on Bundles and Categories -- Vector Bundles -- Relation Between Vector Bundles, Projective Modules, and Idempotents -- K-Theory of Vector Bundles, of Modules, and of Idempotents -- Principal Bundles and Sections of Fibre Bundles: Reduction of the Structure and the Gauge Group I -- Homotopy Classification of Bundles and Cohomology: Classifying Spaces -- Homotopy Classes of Maps and the Homotopy Groups -- The Milnor Construction: Homotopy Classification of Principal Bundles -- Fibrations and Bundles: Gauge Group II -- Cohomology Classes as Homotopy Classes: CW-Complexes -- Basic Characteristic Classes -- Characteristic Classes of Manifolds -- Spin Structures -- Versions of K-Theory and Bott Periodicity -- G-Spaces, G-Bundles, and G-Vector Bundles -- Equivariant K-Theory Functor KG : Periodicity, Thom Isomorphism, Localization, and Completion -- Bott Periodicity Maps and Clifford Algebras -- Gram?Schmidt Process, Iwasawa Decomposition, and Reduction of Structure in Principal Bundles -- Topological Algebras: G-Equivariance and KK-Theory -- Algebra Bundles: Twisted K-Theory -- Isomorphism Classification of Operator Algebra Bundles -- Brauer Group of Matrix Algebra Bundles and K-Groups -- Analytic Definition of Twisted K-Theory -- The Atiyah?Hirzebruch Spectral Sequence in K-Theory -- Twisted Equivariant K-Theory and the Verlinde Algebra -- Gerbes and the Three Dimensional Integral Cohomology Classes -- Bundle Gerbes -- Category Objects and Groupoid Gerbes -- Stacks and Gerbes -- Erratum. 330 $aBased on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comes from quantum field theory, especially string theory, where topological invariants play an important role. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v726 606 $aK-theory 606 $aFiber bundles (Mathematics) 615 0$aK-theory. 615 0$aFiber bundles (Mathematics) 676 $a514.224 700 $aHusemo?ller$b Dale$042117 702 $aHusemo?ller$b Dale 702 $aJurc?o$b Branislav$f1961- 702 $aSchottenloher$b Martin$f1944- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146559803321 996 $aBasic bundle theory and K-cohomology invariants$91016354 997 $aUNINA