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LECTURES ON CHERN-WEIL THEORY AND WITTEN DEFORMATIONS

By (author) Weiping Zhang

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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 Shiingâ€“shen Chern and AndrÃ© Weil, as well as a proof of the Gaussâ€“Bonnetâ€“Chern theorem based on the Mathaiâ€“Quillen construction of Thom forms; the second part presents analytic proofs of the PoincarÃ©â€“Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.

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