The Localization Problem in Index Theory of Elliptic Operators
1st Edition
Published on 11. December 2013
Book
Paperback/Softback
VIII, 117 pages
978-3-0348-0509-4 (ISBN)
Description
The 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 has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.
More details
Product info
Paperback
Series
Edition
2014
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
37
1 farbige Abbildung, 37 s/w Abbildungen
VIII, 117 p. 38 illus., 1 illus. in color.
Dimensions
Height: 240 mm
Width: 168 mm
Thickness: 8 mm
Weight
229 gr
ISBN-13
978-3-0348-0509-4 (9783034805094)
DOI
10.1007/978-3-0348-0510-0
Schweitzer Classification
Other editions
Additional editions
Vladimir Nazaikinskii | Bert-Wolfgang Schulze | Boris Sternin
The Localization Problem in Index Theory of Elliptic Operators
E-Book
11/2013
1st Edition
Birkhäuser
€69.54
Available for download
Content
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.