Equivariant Toeplitz index theory on odd-dimensional manifolds with boundary

TL;DR

This paper develops an equivariant extension of the Toeplitz index theorem for odd-dimensional spin manifolds with boundary, broadening the mathematical understanding of index theory in geometric analysis.

Contribution

It introduces an equivariant Toeplitz index theorem applicable to odd-dimensional manifolds with boundary, extending previous non-equivariant results.

Findings

Established an equivariant Toeplitz index theorem for manifolds with boundary

Extended Dai-Zhang's theorem to odd-dimensional cases

Provided new tools for geometric analysis on manifolds with symmetry

Abstract

In this paper, we establish an equivariant version of Dai-Zhang's Toeplitz index theorem for compact odd-dimensional spin manifolds with even-dimensional boundary.