Equivariant Spectral Flow and Equivariant $\eta$-invariants on Manifolds With Boundary
Abstract
In this article, we study several closely related invariants associated to Dirac operators on odd-dimensional manifolds with boundary with an action of the compact group of isometries. In particular, the equality between equivariant winding numbers, equivariant spectral flow, and equivariant Maslov indices is established. We also study equivariant -invariants which play a fundamental role in the equivariant analog of Getzler's spectral flow formula. As a consequence, we establish a relation between equivariant -invariants and equivariant Maslov triple indices in the splitting of manifolds.
Keywords
Cite
@article{arxiv.2101.01890,
title = {Equivariant Spectral Flow and Equivariant $\eta$-invariants on Manifolds With Boundary},
author = {Johnny Lim and Hang Wang},
journal= {arXiv preprint arXiv:2101.01890},
year = {2024}
}
Comments
35 pages, 15 figures. This article contains results that have direct implications on our second paper arXiv:2101.00193, so it can be viewed as part 1. Revised Introduction, Def. 2.2, Theorem 8.1 statement, and added an example at the end