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Lectures on Chern-Weil theory and Witten deformations [[electronic resource] /] / Weiping Zhang
| Lectures on Chern-Weil theory and Witten deformations [[electronic resource] /] / Weiping Zhang |
| Autore | Zhang Weiping |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (131 p.) |
| Disciplina |
514.72
516.36 |
| Collana | Nankai tracts in mathematics |
| Soggetto topico |
Chern classes
Index theorems Complexes |
| ISBN | 981-238-658-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; Chapter 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; 1.6.1 Chern Forms and Classes; 1.6.2 Pontrjagin Classes for Real Vector Bundles; 1.6.3 Hirzebruch's L-class and A-class; 1.6.4 K-groups and the Chern Character; 1.6.5 The Chern-Simons Transgressed Form; 1.7 Bott Vanishing Theorem for Foliations; 1.7.1 Foliations and the Bott Vanishing Theorem
1.7.2 Adiabatic Limit and the Bott Connection1.8 Chern-Weil Theory in Odd Dimension; 1.9 References; Chapter 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; Chapter 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; Chapter 4 Poincare-Hopf Index Formula: an Analytic Proof 4.1 Review of Hodge Theorem4.2 Poincare-Hopf Index Formula; 4.3 Clifford Actions and the Witten Deformation; 4.4 An Estimate Outside of Up zero(V) Up; 4.5 Harmonic Oscillators on Euclidean Spaces; 4.6 A Proof of the Poincare-Hopf Index Formula; 4.7 Some Estimates for DT,i's, 2 i 4; 4.8 An Alternate Analytic Proof; 4.9 References; Chapter 5 Morse Inequalities: an Analytic Proof; 5.1 Review of Morse Inequalities; 5.2 Witten Deformation; 5.3 Hodge Theorem for ( * (M), dTf; 5.4 Behaviour of rf Near the Critical Points of f; 5.5 Proof of Morse Inequalities; 5.6 Proof of Proposition 5.5 5.7 Some Remarks and Comments5.8 References; Chapter 6 Thom-Smale and Witten Complexes; 6.1 The Thom-Smale Complex; 6.2 The de Rham Map for Thom-Smale Complexes; 6.3 Witten's Instanton Complex and the Map eT; 6.4 The Map P, TeT; 6.5 An Analytic Proof of Theorem 6.4; 6.6 References; Chapter 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; Index |
| Record Nr. | UNINA-9910815738203321 |
Zhang Weiping
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| River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Manifolds with cusps of rank one : spectral theory and L[superscript 2]-index theorem / Werner Muller
| Manifolds with cusps of rank one : spectral theory and L[superscript 2]-index theorem / Werner Muller |
| Autore | Muller, Werner |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, c1987 |
| Descrizione fisica | ix, 158 p. ; 25 cm. |
| Disciplina | 514.74 |
| Collana | Lecture notes in mathematics, 0075-8434 ; 1244 |
| Soggetto topico |
Index theorems
Manifolds Spectral theory |
| ISBN | 3540176969 |
| Classificazione | AMS 58G10 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001099949707536 |
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Muller, Werner
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| Berlin : Springer-Verlag, c1987 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Manifolds with cusps of rank one : spectral theory and L2-index theorem / / Werner Müller
| Manifolds with cusps of rank one : spectral theory and L2-index theorem / / Werner Müller |
| Autore | Müller Werner <1949-> |
| Edizione | [1st ed. 1987.] |
| Pubbl/distr/stampa | Berlin : , : Springer-Verlag, , [1987] |
| Descrizione fisica | 1 online resource (X, 158 p.) |
| Disciplina | 514.74 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico | Index theorems |
| ISBN | 3-540-47762-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Cusps of rank one -- The heat equation on the cusp -- The Neumann laplacian on the cusp -- Manifolds with cusps of rank one -- The spectral resolution of H -- The heat kernel -- The eisenstein functions -- The spectral shift function -- The L2-index of generalized dirac operators -- The unipotent contribution to the index -- The Hirzebruch conjecture. |
| Record Nr. | UNISA-996466383803316 |
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Müller Werner <1949->
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| Berlin : , : Springer-Verlag, , [1987] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Novikov conjectures, index theorems and rigidity : Oberwolfach 1993 / edited by Steven C. Ferry, Andrew Ranicki, Jonathan Rosenberg
| Novikov conjectures, index theorems and rigidity : Oberwolfach 1993 / edited by Steven C. Ferry, Andrew Ranicki, Jonathan Rosenberg |
| Autore | Ferry, Steven C. |
| Pubbl/distr/stampa | Cambridge ; New York : Cambridge University Press, 1995 |
| Descrizione fisica | 2 v. : ill. ; 23 cm |
| Disciplina | 514.3 |
| Altri autori (Persone) |
Ranicki, Andrew
Rosenberg, Jonathan |
| Collana | London Mathematical Society lecture note series, 0076-0552 ; 226 |
| Soggetto topico |
Index theorems
Novikov, Sergei Petrovich Topological manifolds |
| ISBN |
0521497957 (v. 2 : pbk.)
0521497965 (v. 1 : pbk.) |
| Classificazione | AMS 57-06 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001184079707536 |
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Ferry, Steven C.
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| Cambridge ; New York : Cambridge University Press, 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Théorèmes d'indices Gevrey pour les équations différentielles ordinaires / / Jean-Pierre Ramis
| Théorèmes d'indices Gevrey pour les équations différentielles ordinaires / / Jean-Pierre Ramis |
| Autore | Ramis J.-P (Jean-Pierre) |
| Pubbl/distr/stampa | Providence, R.I., USA : , : American Mathematical Society, , [1984] |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina | 515.3/52 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential equations
Index theorems Power series |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0706-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | fre |
| Record Nr. | UNINA-9910480476503321 |
|
Ramis J.-P (Jean-Pierre)
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||
| Providence, R.I., USA : , : American Mathematical Society, , [1984] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Théorèmes d'indices Gevrey pour les équations différentielles ordinaires / / Jean-Pierre Ramis
| Théorèmes d'indices Gevrey pour les équations différentielles ordinaires / / Jean-Pierre Ramis |
| Autore | Ramis J.-P (Jean-Pierre) |
| Pubbl/distr/stampa | Providence, R.I., USA : , : American Mathematical Society, , [1984] |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina | 515.3/52 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential equations
Index theorems Power series |
| ISBN | 1-4704-0706-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | fre |
| Record Nr. | UNINA-9910788887003321 |
|
Ramis J.-P (Jean-Pierre)
|
||
| Providence, R.I., USA : , : American Mathematical Society, , [1984] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Théorèmes d'indices Gevrey pour les équations différentielles ordinaires / / Jean-Pierre Ramis
| Théorèmes d'indices Gevrey pour les équations différentielles ordinaires / / Jean-Pierre Ramis |
| Autore | Ramis J.-P (Jean-Pierre) |
| Pubbl/distr/stampa | Providence, R.I., USA : , : American Mathematical Society, , [1984] |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina | 515.3/52 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential equations
Index theorems Power series |
| ISBN | 1-4704-0706-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | fre |
| Record Nr. | UNINA-9910817128003321 |
|
Ramis J.-P (Jean-Pierre)
|
||
| Providence, R.I., USA : , : American Mathematical Society, , [1984] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Index theorems
(27)
- Geometry, Differential (6)
- Chern classes (3)
- Complexes (3)
- Diffeomorphisms (3)