Lectures on Chern-Weil theory and Witten Deformations / Weiping Zhang.
Material type:
TextPublication details: River Edge, N.J. : World Scientific, c2001.Description: xi, 117 p. ; 22 cmISBN: - 9810246862 (pbk.)
- 9810246854
- QA613.618 .Z43 2001
| Item type | Current library | Call number | Copy number | Status | Barcode | |
|---|---|---|---|---|---|---|
| Books | Library First Floor | QA613.618 .Z43 2001 (Browse shelf(Opens below)) | 1 | Available | 9561 |
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| QA613 .L44 2003 Introduction to Smooth Manifolds / | QA613.2 .L44 2000 Introduction to topological manifolds / | QA613.618 .M54 1974 Characteristic Classes, | QA613.618 .Z43 2001 Lectures on Chern-Weil theory and Witten Deformations / | QA613.62 .N54 2001 Foliations on Surfaces / | QA614.3 .B53 2001 Riemannian Geometry of Contact and Symplectic Manifolds / | QA614.3 .W45 2008 Differential Analysis on Complex Manifolds / |
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.
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