Ebook: Spectral Flow: A Functional Analytic and Index-Theoretic Approach

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