Cargando…

The Index Theorem and The Heat Equation Method.

This volume provides a self-contained represenation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first-order geometric elliptic operators by using the heat-equation method. The proofs are up...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: World Scientific 2001.
Temas:
Acceso en línea:Texto completo

MARC

LEADER 00000cam a2200000M 4500
001 EBOOKCENTRAL_ocn815754701
003 OCoLC
005 20240329122006.0
006 m o d
007 cr un|---uuuuu
008 121012s2001 xx o 000 0 eng d
040 |a IDEBK  |b eng  |e pn  |c IDEBK  |d OCLCQ  |d EBLCP  |d OCLCQ  |d DEBSZ  |d OCLCQ  |d MERUC  |d ZCU  |d U3W  |d OCLCO  |d OCLCF  |d STF  |d ICG  |d INT  |d OCLCQ  |d TKN  |d OCLCQ  |d DKC  |d OCLCQ  |d UKAHL  |d OCLCQ  |d VLY  |d OCLCO  |d OCLCQ  |d OCLCO  |d OCLCL 
020 |a 1281951641 
020 |a 9781281951649 
020 |a 9789812810106 
020 |a 9812810102 
029 1 |a AU@  |b 000051372778 
029 1 |a AU@  |b 000058360641 
029 1 |a DEBBG  |b BV044178820 
029 1 |a DEBSZ  |b 405244592 
035 |a (OCoLC)815754701 
050 4 |a JF1525 
072 7 |a PBPH  |2 bicssc 
082 0 4 |a 514.74 
049 |a UAMI 
245 0 4 |a The Index Theorem and The Heat Equation Method. 
260 |b World Scientific  |c 2001. 
300 |a 1 online resource 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
520 |a This volume provides a self-contained represenation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first-order geometric elliptic operators by using the heat-equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems. 
505 0 |a PREFACE; CONTENTS; DEFINITIONS AND FORMULAS; CHAPTER 1 PRELIMINARIES IN RIEMANNIAN GEOMETRY; 1.1 Basic Notions of Riemannian Geometry; 1.2 Computations by using Orthonormal Moving Frame; 1.3 Differential Forms and Orthonormal Moving Frame Method; 1.4 Classical Geometric Operators; 1.5 Normal Coordinates; 1.6 Computations on Sphere; 1.7 Connections on Vector Bundles and Principal Bundles; 1.8 General Tensor Calculus; CHAPTER 2 SCHRODINGER AND HEAT OPERATORS; 2.1 Fundamental Solution and Levi Iteration; 2.2 Existence of Fundamental Solution; 2.3 Cauchy Problem of Heat Equation 
505 8 |a 2.4 Hodge Theorem2.5 Applications of Hodge Theorem; 2.6 Index Problem; CHAPTER 3 MP PARAMETRIX AND APPLICATIONS; 3.1 MP Parametrix; 3.2 Existence of Initial Solutions; 3.3 Asymptotic Expansion for Heat Kernel; 3.4 Local Index for Elliptic Operators; CHAPTER 4 CHERN-WEIL THEORY; 4.1 Characteristic Forms and Characteristic Classes; 4.2 General Characteristic Forms; 4.3 Chern Root Algorithm; 4.4 Formal Approach to Local Index of Signature Operator; CHAPTER 5 CLIFFORD ALGEBRA AND SUPER ALGEBRA; 5.1 Clifford Algebra; 5.2 Super Algebra; 5.3 Computations on Supertraces; CHAPTER 6 DIRAC OPERATOR 
505 8 |a 6.1 Spin Structure6.2 Spinor Bundle; 6.3 Dirac Operator; 6.4 Index of Dirac Operator; CHAPTER 7 LOCAL INDEX THEOREMS; 7.1 Local Index Theorem for Dirac Operator; 7.2 Local Index Theorem for Signature Operator; 7.3 Local Index Theorem for de Rham-Hodge Operator; CHAPTER 8 RIEMANN-ROCH THEOREM; 8.1 Hermitian Metric; 8.2 Hermitian Connection; 8.3 Riemann-Roch Operator; 8.4 Weitzenbock Formula; 8.5 Index Theorem; 8.6 Riemann-Roch Operator in Complex Analysis; REFERENCES; INDEX 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Atiyah-Singer index theorem. 
650 0 |a Heat equation. 
650 6 |a Théorème d'Atiyah-Singer. 
650 6 |a Équation de la chaleur. 
650 7 |a Atiyah-Singer index theorem  |2 fast 
650 7 |a Heat equation  |2 fast 
720 |a Yu, Y.L. 
758 |i has work:  |a The index theorem and the heat equation method (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGVJYjp3Qr9BPpVYbmKJH3  |4 https://id.oclc.org/worldcat/ontology/hasWork 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1679404  |z Texto completo 
938 |a Askews and Holts Library Services  |b ASKH  |n AH24685521 
938 |a EBL - Ebook Library  |b EBLB  |n EBL1679404 
938 |a ProQuest MyiLibrary Digital eBook Collection  |b IDEB  |n 195164 
994 |a 92  |b IZTAP