Overview

This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing–shen Chern and André Weil, as well as a proof of the Gauss–Bonnet–Chern theorem based on the Mathai–Quillen construction of Thom forms; the second part presents analytic proofs of the Poincaré–Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.Contents: Chern–Weil Theory for Characteristic ClassesBott and Duistermaat–Heckman FormulasGauss–Bonnet–Chern TheoremPoincaré–Hopf Index Formula: An Analytic ProofMorse Inequalities: An Analytic ProofThom–Smale and Witten ComplexesAtiyah Theorem on Kervaire Semi-characteristicReadership: Graduate students and researchers in differential geometry, topology and mathematical physics.

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9781299990852

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