1. Eta and rho invariants on manifolds with edges
- Author
-
Boris Vertman and Paolo Piazza
- Subjects
spin manifold ,Mathematics - Differential Geometry ,Pure mathematics ,incomplete edge metrics ,Microlocal analysis ,Boundary (topology) ,58J52 ,Dirac operator ,01 natural sciences ,Mathematics - Spectral Theory ,symbols.namesake ,Fredholm index ,Mathematics::K-Theory and Homology ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,signature operator ,Spectral Theory (math.SP) ,Heat kernel ,Mathematics ,Algebra and Number Theory ,Mathematics::Operator Algebras ,Dirac (video compression format) ,010102 general mathematics ,stratified space ,Eta invariant ,heat kernel asymptotic ,Rho invariant ,spin dirac operator ,Differential Geometry (math.DG) ,symbols ,010307 mathematical physics ,Geometry and Topology ,Mathematics::Differential Geometry ,Signature (topology) ,Edge space ,Atiyah–Singer index theorem - 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., 65 pages, 2 figures
- Published
- 2016