TY  - BOOK
AU  - Zhang,Weiping
TI  - Lectures on Chern-Weil theory and Witten Deformations
SN  - 9810246862 (pbk.)
AV  - QA613.618 .Z43 2001
PY  - 2001///
CY  - River Edge, N.J.
PB  - World Scientific
KW  - Chern classes
KW  - Index theorems
KW  - Complexes
N1  - Includes bibliographical references and index; 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
N2  - 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
ER  -