Zhang, Weiping,  1964- <br/><br/>
Lectures on Chern-Weil theory and Witten Deformations / 
Weiping Zhang. 
 - River Edge, N.J. :  World Scientific,  c2001. 
 - xi, 117 p. ;  22 cm. 
<br/><br/>Includes bibliographical references and index. 
<br/><br/>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. 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9810246862 (pbk.) 9810246854 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Chern classes.<br/>Index theorems.<br/>Complexes.
<br/><br/><label>LC Class. No.: </label>QA613.618  / .Z43 2001