Weiping Zhang, Zhang Wei-Ping “Lectures on Chern-Weil Theory and Witten Deformations ”
World Scientific Publishing Company | 2002-01-15 | ISBN: 9810246854 | 110 pages | PDF | 3,2 Mb

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.

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