Lectures on Chern-Weil Theory and Witten Deformations

✍ Scribed by Weiping Zhang, Zhang Wei-Ping

• Publisher: World Scientific Publishing Company
• Year: 2002
• Tongue: English
• Leaves: 131
• Edition: 1st
• Category: Library

✦ Synopsis

Based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics, this volume consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and Andr 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 Poincar-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.