Lectures on Chern-Weil Theory and Witten Deformations

✍ Scribed by Weiping Zhang, Zhang Wei-Ping

• Publisher: World Scientific
• Year: 2001
• Tongue: English
• Leaves: 131
• Series: Nankai tracts in mathematics 4
• Edition: 1st
• Category: Library

✦ Synopsis

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 Andre 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.