Lectures on Chern-Weil Theory and Witten Deformations

ISBN-13: 9789810246860 / Angielski / Miękka / 2001 / 132 str.

Zhang Wei-Ping; Weiping Zhang

Opis

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.