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arXiv · 2101.01890

Equivariant Spectral Flow and Equivariant $\eta$-invariants on Manifolds With Boundary

Johnny Lim·Hang Wang
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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 $H$ of isometries. In particular, the equality between equivariant winding numbers, equivariant spectral flow, and equivariant Maslov indices is established. We also study equivariant $\eta$-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 $\eta$-invariants and equivariant Maslov triple indices in the splitting of manifolds.

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Johnny Lim, Hang Wang. 2021-01-06. Equivariant Spectral Flow and Equivariant $\eta$-invariants on Manifolds With Boundary. https://doi.org/10.1142/s0129167x2450006x

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