Titlebook: Differential Geometry and Mathematical Physics; Part II. Fibre Bundl Gerd Rudolph,Matthias Schmidt Book 2017 Springer Science+Business Medi

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grandiose

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Accolade

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Cohomology Theory of Fibre Bundles. Characteristic Classes,d Stiefel-Whitney classes. Moreover, we discuss theWeil homomorphism, which provides a geometric description of characteristic classes in terms of de Rham cohomology, and genera of vector bundles. Finally, we explain a method to construct an approximation of the classifying space in terms of Eilenberg-MacLane spaces, known as the Postnikov tower.

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Clifford Algebras, Spin Structures and Dirac Operators,ed the Dirac operator. We study the theory of Dirac operators in a systematic way, including the Hodge Decomposition Theorem, Weitzenboeck formulae and the classical elliptic complexes. The chapter culminates in a proof of the Atiyah-Singer Index Theorem via the heat kernel method and includes applications to the classical complexes.