The localization problem in index theory of elliptic operators /

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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Sábháilte in:
Sonraí bibleagrafaíochta
Príomhchruthaitheoir: Nazaikinskii, Vladimir (Údar)
Údar corparáideach: SpringerLink (Online service)
Rannpháirtithe: Schulze, Bert-Wolfgang, Sternin, Boris
Formáid: Ríomhleabhar
Teanga:English
Foilsithe / Cruthaithe: Basel Springer Basel 2014.
Sraith:Pseudo-Differential Operators, Theory and Applications ; 10
Ábhair:
Mathematics.
K-theory.
Functional analysis.
Global analysis.
Differential equations, Partial.
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Clár na nÁbhar:
  • 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.

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