Lectures On Chern-weil Theory And Witten Deformations
Seiten
2001
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-4686-0 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-4686-0 (ISBN)
Based on the notes of a graduate course on differential geometry, this volume contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and Andr Weil, as well as presenting the Morse inequalities based on deformations introduced by Edward Witten.
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.
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.
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.
| Erscheint lt. Verlag | 25.9.2001 |
|---|---|
| Reihe/Serie | Nankai Tracts in Mathematics ; 4 |
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 981-02-4686-2 / 9810246862 |
| ISBN-13 | 978-981-02-4686-0 / 9789810246860 |
| Zustand | Neuware |
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