Lectures on Chern-Weil theory and Witten Deformations /
Zhang, Weiping, 1964-
Lectures on Chern-Weil theory and Witten Deformations / Weiping Zhang. - River Edge, N.J. : World Scientific, c2001. - xi, 117 p. ; 22 cm.
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.
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.
9810246862 (pbk.) 9810246854
Chern classes.
Index theorems.
Complexes.
QA613.618 / .Z43 2001
Lectures on Chern-Weil theory and Witten Deformations / Weiping Zhang. - River Edge, N.J. : World Scientific, c2001. - xi, 117 p. ; 22 cm.
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.
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.
9810246862 (pbk.) 9810246854
Chern classes.
Index theorems.
Complexes.
QA613.618 / .Z43 2001