Basic bundle theory and K-cohomology invariants/
Dale Husemoller, Michael Joachim, Branislav Jurco and Martin Schottenloher
- Berlin: Springer, c2008.
- xv, 340 p. : ill. ; 25 cm.
- (Lecture notes in physics), 726 .
Physical background to the k-theory classification of D-Branes: introduction and references -- pt. I Bundles over a space and modules over an algebra -- Generalities on bundles and categories -- Vector bundles -- Relation between vector bundles, projective modules, and indempotents -- K-theory of vector bundles and sections of fibre bundles: reduction of the structure and the guage group I -- pt. II. Homotopy classification of bundles and cohomolgy: 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 -- pt. III. Versions of K-theory and bott periodicity -- G-spaces, G-bundles, and G-vector bundles -- Equivariant K-theory functor K(subscript G) : periodicity, thom isomorphism, localization, and completion -- Bott periodicity maps and Clifford algebras -- Gram-Schmidt process, Iwasawa decomposition, and reduction of structure -- Topological algebras: G-equivariance and KK-theory -- pt. IV. 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 Velinde algebra -- pt. V. Gerbes and the three dimensional integral cohomology classes -- Bundle grebes -- Category objects and groupoid gerbs -- Stack and grebes.