Approximation of delocalized eta invariants by their finite analogues

Abstract: The delocalized eta invariant for self-adjoint elliptic operators was introduced by Lott as a natural extension of the classical eta invariant of Atiyah-Patodi-Singer. In this talk, we will give several results on when the delocalized eta invariant can be approximated by the ones associated with finite-sheeted covering spaces, under a necessary assumption of conjugacy distinguishability. In the first part, we will present a result using a K-theoretical approach of the delocalized eta invariant. In the second part, we will give a quantized description of conjugacy distinguishability. This is a joint work with Zhizhang Xie and Guoliang Yu.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

( paper )

Göttingen topology and geometry seminar

Series comments: Our seminar takes place via zoom every Tuesday afternoon (Central European Summer Time; the precise time slot varies—please always refer to the listing).