Eta and rho invariants on manifolds with edges
Differential Geometry
2020-03-03 v2 Spectral Theory
Abstract
We establish existence of the eta-invariant as well as of the Atiyah-Patodi-Singer and the Cheeger-Gromov rho-invariants for a class of Dirac operators on an incomplete edge space. Our analysis applies in particular to the signature, the Gauss-Bonnet and the spin Dirac operator. We derive an analogue of the Atiyah-Patodi-Singer index theorem for incomplete edge spaces and their non-compact infinite Galois coverings with edge singular boundary. Our arguments employ microlocal analysis of the heat kernel asymptotics on incomplete edge spaces and the classical argument of Atiyah-Patodi-Singer. As an application, we discuss stability results for the two rho-invariants we have defined.
Keywords
Cite
@article{arxiv.1604.07420,
title = {Eta and rho invariants on manifolds with edges},
author = {Paolo Piazza and Boris Vertman},
journal= {arXiv preprint arXiv:1604.07420},
year = {2020}
}
Comments
65 pages, 2 figures