Introduction to Characteritic Classes and Index Theory
by Jean-Pierre Schneiders
Publisher: Universidade de Lisboa 2000
Number of pages: 236
This text deals with characteristic classes of real and complex vector bundles and Hirzebruch-Riemann-Roch formula. We will present a few basic but fundamental facts which should help the reader to gain a good idea of the mathematics involved. The reader is assumed to have a good knowledge of homological algebra and topology.
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Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
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In this book the authors present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various proofs.