Lectures On Chern-weil Theory And Witten Deformations: 4 (Nankai Tracts in Mathematics) - Hardcover

Zhang, Weiping

Hardcover

ISBN 10: 9810246854 ISBN 13: 9789810246853

Publisher: World Scientific Publishing Co Pte Ltd, 2001

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 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.

About this title

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.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 2001
• ISBN 10: 9810246854
• ISBN 13: 9789810246853
• Binding: Hardcover
• Language: English
• Number of pages: 132