000			01709cam a22002654a 4500
001			vtls000001801
003			VRT
005			20250102222428.0
008			081110s2001 nju |b 001 0 eng
020			_a9810246862 (pbk.)
020			_a9810246854
039		9	_a201402040055 _bVLOAD _c201007311141 _dmalmash _c200811101443 _dvenkatrajand _c200811100914 _dNoora _y200811100912 _zNoora
050	0	0	_aQA613.618 _b.Z43 2001
100	1		_aZhang, Weiping, _d1964- _91238
245	1	0	_aLectures on Chern-Weil theory and Witten Deformations / _cWeiping Zhang.
260			_aRiver Edge, N.J. : _bWorld Scientific, _cc2001.
300			_axi, 117 p. ; _c22 cm.
504			_aIncludes bibliographical references and index.
505			_aChern-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.
520			_aBased 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.
650		0	_aChern classes. _91239
650		0	_aIndex theorems. _91240
650		0	_aComplexes. _91241
942			_2lcc _n0 _cBK
999			_c361 _d361