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Basic bundle theory and K-cohomology invariants/ Dale Husemoller, Michael Joachim, Branislav Jurco and Martin Schottenloher

By: Husemoller, DaleContributor(s): Joachim, Michael | Jurco, Branislav | Schottenloher, MartinMaterial type: Text

TextSeries: (Lecture notes in physics) ; 726Publication details: Berlin: Springer, c2008Description: xv, 340 p. : ill. ; 25 cmISBN: 9783540749554Subject(s): K-theory | Mathematical physics | Algebra | MathematicsDDC classification: 514.23

Contents:

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.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	514.23 HUS/B (Browse shelf(Opens below))	Available		P25257

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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.

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