Lectures on Chern-Weil Theory and Witten Deformations

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.

List of contents

Chern-Weil theory for characteristic classes; Bott and Duistermaat-Heckman formulas; Gauss-Bonnet-Chern theorem; Poincar -Hopf index formula - an analytic proof; morse inequalities - an analytic proof; Thom-Smale and Witten complexes; Atiyah theorem on Kervaire Semi-characteristic.

Product details

• Authors: Weiping Zhang
• Publisher: World Scientific Publishing Company
• Languages: English
• Product format: Paperback / Softback
• Released: 25.09.2001
• EAN: 9789810246860
• ISBN: 978-981-02-4686-0
• No. of pages: 132
• Dimensions: 150 mm x 209 mm x 10 mm
• Weight: 192 g
• Series: Nankai Tracts in Mathematics; Nankai Tracts in Mathematics; Nankai Tracts in Mathematics (
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra