In this thesis, we propose a novel notion of the spectral flow in an equivariant setting, where a locally compact, unimodular group acts properly and isometrically on a Riemannian manifold. This new notion, which we call G-spectral flow, is introduced here for families of equivariant Dirac-type and Toeplitz operators, and is given by a class in the K-theory of the group C*-algebra. In the context of the fundamental group of a compact manifold acting on its universal cover, we show that G-spectral flow refines the classical notion via an integration map. Our main results are index theorems, generalising the classical theory of spectral flow of operators to the equivariant setting.

Contains fulltext : 317235.pdf (Publisher’s version ) (Open Access)

Promotor : Suijlekom, W.D. van Co-promotor : Hochs, P.

Radboud University, 11 maart 2025

137 p.