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arXiv · 1604.07420

Eta and rho invariants on manifolds with edges

Paolo Piazza·Boris Vertman
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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.

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Paolo Piazza, Boris Vertman. 2018-12-13. Eta and rho invariants on manifolds with edges. https://arxiv.org/abs/1604.07420

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