An index theorem for end-periodic operators
Differential Geometry
2019-02-20 v3 Analysis of PDEs
Geometric Topology
Abstract
We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes' Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah-Patodi-Singer eta-invariant in the cylindrical setting. We apply this periodic eta-invariant to the study of moduli spaces of Riemannian metrics of positive scalar curvature.
Cite
@article{arxiv.1105.0260,
title = {An index theorem for end-periodic operators},
author = {Tomasz Mrowka and Daniel Ruberman and Nikolai Saveliev},
journal= {arXiv preprint arXiv:1105.0260},
year = {2019}
}
Comments
72 pages; extended and expanded from earlier versions. Introduction of twisted eta invariants with applications to moduli of metrics of positive scalar curvature