Lectures on Chern-Weil Theory and Witten Deformations (Nankai Tracts in Mathematics v. 4)

Lectures on Chern-Weil Theory and Witten Deformations (Nankai Tracts in Mathematics v. 4)

By: Weiping Zhang (author)Hardback

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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 Andre 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 Poincare-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.

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Contents

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.

Product Details

  • publication date: 25/09/2001
  • ISBN13: 9789810246853
  • Format: Hardback
  • Number Of Pages: 132
  • ID: 9789810246853
  • ISBN10: 9810246854

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