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121012s2001 xx o 000 0 eng d |
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|a 1281951641
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|a 9781281951649
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|a 9789812810106
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|a 9812810102
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|a DEBSZ
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|a (OCoLC)815754701
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|a JF1525
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|a PBPH
|2 bicssc
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|a 514.74
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|a UAMI
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|a The Index Theorem and The Heat Equation Method.
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|b World Scientific
|c 2001.
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|a 1 online resource
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|a text
|b txt
|2 rdacontent
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|a online resource
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|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.
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|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
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|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
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|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
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|a ProQuest Ebook Central
|b Ebook Central Academic Complete
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|a Atiyah-Singer index theorem.
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|a Heat equation.
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|a Théorème d'Atiyah-Singer.
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|a Équation de la chaleur.
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|a Atiyah-Singer index theorem
|2 fast
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|a Heat equation
|2 fast
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|a Yu, Y.L.
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|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
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|u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1679404
|z Texto completo
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|a Askews and Holts Library Services
|b ASKH
|n AH24685521
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|a EBL - Ebook Library
|b EBLB
|n EBL1679404
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938 |
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|a ProQuest MyiLibrary Digital eBook Collection
|b IDEB
|n 195164
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994 |
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|a 92
|b IZTAP
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