MARC Record from marc_columbia

LEADER: 05141cam a2200637Ma 4500
001 4252255
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008 030815s2001 nju ob 001 0 eng d
035 $a(OCoLC)ocn646768373
035 $a(NNC)4252255
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049 $aZCUA
100 1 $aZhang, Weiping,$d1964-
245 10 $aLectures on Chern-Weil theory and Witten deformations /$cWeiping Zhang.
260 $aRiver Edge, N.J. :$bWorld Scientific,$c©2001.
300 $a1 online resource (xi, 117 pages).
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aNankai tracts in mathematics ;$v4
504 $aIncludes bibliographical references and index.
588 0 $aPrint version record.
505 0 $aCh. 1. Chern-Weil theory for characteristic classes. 1.1. Review of the de Rham cohomology theory. 1.2. Connections on vector bundles. 1.3. The curvature of a connection. 1.4. Chern-Weil theorem. 1.5. Characteristic forms, classes and numbers. 1.6. Some examples. 1.7. Bott vanishing theorem for foliations. 1.8. Chern-Weil theory in odd dimension. 1.9. References -- ch. 2. Bott and Duistermaat-Heckman formulas. 2.1. Berline-Vergne localization formula. 2.2. Bott residue formula. 2.3. Duistermaat-Heckman formula. 2.4. Bott's original idea. 2.5. References -- ch. 3. Gauss-Bonnet-Chern theorem. 3.1. A toy model and the Berezin integral. 3.2. Mathai-Quillen's Thom form. 3.3. A transgression formula. 3.4. Proof of the Gauss-Bonnet-Chern theorem. 3.5. Some remarks. 3.6. Chern's original proof. 3.7. References -- ch. 4. Poincaré-Hopf index formula: an analytic proof. 4.1. Review of Hodge theorem. 4.2. Poincaré-Hopf index formula. 4.3. Clifford actions and the Witten deformation. 4.4. An estimate outside of [symbol]. 4.5. Harmonic oscillators on Euclidean spaces. 4.6. A proof of the Poincaré-Hopf index formula. 4.7. Some estimates for [symbol]. 4.8. An alternate analytic proof. 4.9. References -- ch. 5. Morse inequalities: an analytic proof. 5.1. Review of Morse inequalities. 5.2. Witten deformation. 5.3. Hodge theorem for ([symbol]). 5.4. Behaviour of [symbol] near the critical points of f. 5.5. Proof of Morse inequalities. 5.6. Proof of proposition 5.5. 5.7. Some remarks and comments. 5.8. References -- ch. 6. Thom-Smale and Witten complexes. 6.1. The Thorn-Smale complex. 6.2. The de Rham map for Thom-Smale complexes. 6.3. Witten's instanton complex and the map [symbol]. 6.4. The map [symbol]. 6.5. An analytic proof of theorem 6.4. 6.6. References -- ch. 7. Atiyah theorem on Kervaire semi-characteristic. 7.1. Kervaire semi-characteristic. 7.2. Atiyah's original proof. 7.3. A proof via Witten deformation. 7.4. A generic counting formula for k(M). 7.5. Non-multiplicativity of k(M). 7.6. References.
520 $aThis 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.
650 0 $aChern classes.
650 0 $aIndex theorems.
650 0 $aComplexes.
650 6 $aClasses de Chern.
650 6 $aThéorèmes d'indices.
650 6 $aComplexes (Mathématiques)
650 7 $aMATHEMATICS$xTopology.$2bisacsh
650 07 $aIndex theorems.$2cct
650 07 $aComplexes.$2cct
650 07 $aChern classes.$2cct
650 7 $aChern classes.$2fast$0(OCoLC)fst00853646
650 7 $aComplexes.$2fast$0(OCoLC)fst00871597
650 7 $aIndex theorems.$2fast$0(OCoLC)fst00968961
655 0 $aElectronic books.
655 4 $aElectronic books.
776 08 $iPrint version:$aZhang, Weiping.$tLectures on Chern-Weil theory and Witten deformations.$dRiver Edge, N.J. : World Scientific, ©2001$w(DLC) 2001046629
830 0 $aNankai tracts in mathematics ;$vv. 4.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio4252255$zAll EBSCO eBooks
852 8 $blweb$hEBOOKS