Lectures On Chern-weil Theory And Witten Deformations

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.

Sommario

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.

Dettagli sul prodotto

• Autori: Weiping Zhang, Zhang Weiping
• Editore: Ingram Publishers Services
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 25.09.2001
• EAN: 9789810246860
• ISBN: 978-981-02-4686-0
• Serie: Nankai Tracts in Mathematics; Nankai Tracts in Mathematics; Nankai Tracts in Mathematics (
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Aritmetica, algebra; SCIENCE / Physics / General, MATHEMATICS / Geometry / Differential, MATHEMATICS / Topology, Physics, Topology, Differential & Riemannian geometry, Differential and Riemannian geometry