Doll N. Spectral Flow. A Functional Analytic and Index-Theoretic Approach 2023

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Doll N. Spectral Flow. A Functional Analytic and Index-Theoretic Approach 2023

Textbook in PDF format 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 Preface Acknowledgment Spectral flow in finite dimension Applications of finite-dimensional spectral flow Bounded Fredholm operators Spectral flow for bounded self-adjoint Fredholm operators Fredholm pairs and their index Unbounded Fredholm operators Spectral flow for unbounded self-adjoint Fredholm operators Homotopy theory of Fredholm operators Bott–Maslov index via spectral flow Index pairings and spectral localizer Spectral flow in semifinite von Neumann algebras Spectral flow in bifurcation theory A Collection of technical elements Acronyms and notations Bibliography Index