Spectral Flow A Functional Analytic and Index-Theoretic Approach - Doll, Nora (De Gruyter Studies in Mathematics, 2023)
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 semi finite sense. The importance of spectral flow for homotopy and index theory are discussed in detail. Applications concern eta-invariants, the Bott-Maslov and Conley-Zehnder indices, Sturm-Liouville oscillation theory, the spectral localizer and bifurcation theory.