Lectures on Chern-Weil Theory and Witten Deformations by Weiping Zhang (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “The book gives an excellent introduction to these analytic techniques” — Mathematical Reviews, 2002This book is noteworthy for its combination of brevity, clarity, accessibility, and depth. — Mathematics Abstracts From the Publisher Readership: Graduate students and researchers in differential geometry, topology and mathematical physics

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