The localization problem in index theory of elliptic operators /
This book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions ha...
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| Format: | eBook |
| Language: | English |
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Basel
Springer Basel
2014.
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| Series: | Pseudo-Differential Operators, Theory and Applications ;
10 |
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| Online Access: | Click here to view the full text content |
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Table of Contents:
- Preface
- Introduction
- 0.1 Basics of Elliptic Theory
- 0.2 Surgery and the Superposition Principle
- 0.3 Examples and Applications
- 0.4 Bibliographical Remarks
- Part I: Superposition Principle
- 1 Superposition Principle for the Relative Index
- 1.1 Collar Spaces
- 1.2 Proper Operators and Fredholm Operators
- 1.3 Superposition Principle
- 2 Superposition Principle for K-Homology
- 2.1 Preliminaries
- 2.2 Fredholm Modules and K-Homology
- 2.3 Superposition Principle
- 2.4 Fredholm Modules and Elliptic Operators
- 3 Superposition Principle for KK-Theory
- 3.1 Preliminaries
- 3.2 Hilbert Modules, Kasparov Modules, and KK
- 3.3 Superposition Principle
- Part II: Examples
- 4 Elliptic Operators on Noncompact Manifolds
- 4.1 Gromov-Lawson Theorem
- 4.2 Bunke Theorem
- 4.3 Roe's Relative Index Construction
- 5 Applications to Boundary Value Problems
- 5.1 Preliminaries
- 5.2 Agranovich-Dynin Theorem
- 5.3 Agranovich Theorem
- 5.4 Bojarski Theorem and Its Generalizations
- 5.5 Boundary Value Problems with Symmetric Conormal Symbol
- 6 Spectral Flow for Families of Dirac Type Operators
- 6.1 Statement of the Problem
- 6.2 Simple Example
- 6.3 Formula for the Spectral Flow
- 6.4 Computation of the Spectral Flow for a Graphene Sheet
- Bibliography.