Book
Open Access
Spectral Flow
A Functional Analytic and Index-Theoretic Approach
-
Nora Doll
Language:
English
Published/Copyright:
2023
About this book
Open Access
This is the first treatment entirely dedicated to an analytic study of spectral flow for paths of selfadjoint Fredholm operators, possibly unbounded or understood in a semifinite sense. The importance of spectral flow for homotopy and index theory is discussed in detail. Applications concern eta-invariants, the Bott-Maslov and Conley-Zehnder indices, Sturm-Liouville oscillation theory, the spectral localizer and bifurcation theory.
- Presents a self-contained functional analytic treatment of spectral flow
- Includes a detailed analysis of the homotopy theory of the set of unbounded selfadjoint Fredholm operators
- Provides an analysis of Bott-Maslov index via spectral flow
Author / Editor information
Nora Doll, Hermann Schulz-Baldes, FAU Erlangen-Nürnberg; Nils Waterstraat, MLU Halle-Wittenberg, Germany.
Topics
-
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Frontmatter
I -
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Preface
V -
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Acknowledgment
XIII -
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Contents
XV -
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1 Spectral flow in finite dimension
1 -
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2 Applications of finite-dimensional spectral flow
25 -
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3 Bounded Fredholm operators
64 -
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4 Spectral flow for bounded self-adjoint Fredholm operators
89 -
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5 Fredholm pairs and their index
126 -
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6 Unbounded Fredholm operators
173 -
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7 Spectral flow for unbounded self-adjoint Fredholm operators
218 -
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8 Homotopy theory of Fredholm operators
247 -
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9 Bott–Maslov index via spectral flow
277 -
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10 Index pairings and spectral localizer
313 -
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11 Spectral flow in semifinite von Neumann algebras
345 -
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12 Spectral flow in bifurcation theory
389 -
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A Collection of technical elements
417 -
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Acronyms and notations
427 -
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Bibliography
431 -
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Index
439
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 19, 2023
eBook ISBN:
9783111172477
Hardcover published on:
June 19, 2023
Hardcover ISBN:
9783111169897
Pages and Images/Illustrations in book
Front matter:
18
Main content:
442
Illustrations:
4
Keywords for this book
Self-adjoint Fredholm operators; topologies thereon; Index theory of Fredholm pairs; Bott-Maslov and Conley-Zehnder indices; Oscillation theory Jacobi operators; scattering theory; Variational bifurcation theory
Audience(s) for this book
Institutional Libraries, graduate students and researchers studying spectral flows.
Creative Commons
BY-NC-ND 4.0
Safety & product resources
-
Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
