Vector Bundles K Theory by Allen Hatcher

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Vector Bundles K Theory written by Allen Hatcher This is an other great mathematics book cover the following topics.

Vector Bundles
Basic Definitions and Constructions, Sections, Direct Sums, Inner Products, Tensor Products, Associated Fiber Bundles, Classifying Vector Bundles, Pullback Bundles 18. Clutching Functions 22. The Universal Bundle, Cell Structures on Grassmannians, Appendix: Paracompactness

K–Theory The Functor K(X), Ring Structure, The Fundamental Product Theorem, Bott Periodicity, Exact Sequences 51. Deducing Periodicity from the Product Theorem, Extending to a Cohomology Theory, Division Algebras and Parallelizable Spheres, H–Spaces, Adams Operations, The Splitting Principle, Bott Periodicity in the Real Case [not yet written], Vector Fields on Spheres [not yet written]

Characteristic Classes
Stiefel-Whitney and Chern Classes, Axioms and Constructions, Cohomology of Grassmannians, Euler and Pontryagin Classes, The Euler Class 91. Pontryagin Classes, Characteristic Classes as Obstructions

The J–Homomorphism
Lower Bounds on Im J, The Chern Character, The e Invariant, Thom Spaces, Bernoulli Denominators, Upper Bounds on Im J [not yet written]

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