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

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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