Spectral Flow: A Functional Analytic and Index-Theoretic Approach

Nora Doll; Hermann Schulz-Baldes; Nils Waterstraat

Open Access Published by De Gruyter 2023

Spectral Flow

A Functional Analytic and Index-Theoretic Approach

Nora Doll , Hermann Schulz-Baldes and Nils Waterstraat

Volume 94 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783111172477

Overview
Contents

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

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Acknowledgment Publicly Available Download PDF	XIII
Contents Publicly Available Download PDF	XV
1 Spectral flow in finite dimension Open Access Download PDF	1
2 Applications of finite-dimensional spectral flow Open Access Download PDF	25
3 Bounded Fredholm operators Open Access Download PDF	64
4 Spectral flow for bounded self-adjoint Fredholm operators Open Access Download PDF	89
5 Fredholm pairs and their index Open Access Download PDF	126
6 Unbounded Fredholm operators Open Access Download PDF	173
7 Spectral flow for unbounded self-adjoint Fredholm operators Open Access Download PDF	218
8 Homotopy theory of Fredholm operators Open Access Download PDF	247
9 Bott–Maslov index via spectral flow Open Access Download PDF	277
10 Index pairings and spectral localizer Open Access Download PDF	313
11 Spectral flow in semifinite von Neumann algebras Open Access Download PDF	345
12 Spectral flow in bifurcation theory Open Access Download PDF	389
A Collection of technical elements Open Access Download PDF	417
Acronyms and notations Open Access Download PDF	427
Bibliography Open Access Download PDF	431
Index Open Access Download PDF	439

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Institutional Libraries, graduate students and researchers studying spectral flows.
Pages
- Front matter: 18
- Main content: 442
Illustrations
- Illustrations: 4
Keywords: 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

eBook

Published: June 19, 2023
ISBN: 9783111172477

Hardcover

Published: June 19, 2023
ISBN: 9783111169897