Dirac-operators and symmetries of quasitoric manifolds

TL;DR

This paper proves a vanishing theorem for twisted Dirac operator indices on Spin^c-manifolds with non-abelian symmetries and applies it to bound the symmetry degree of quasitoric manifolds.

Contribution

It introduces a new vanishing result for Dirac indices under non-abelian group actions and uses it to analyze symmetries of quasitoric manifolds.

Findings

Vanishing of Dirac indices under certain non-abelian symmetries

Upper bounds for symmetry degrees of quasitoric manifolds

Application of index theory to geometric symmetry analysis

Abstract

We establish a vanishing result for indices of certain twisted Dirac operators on $\text{Spin}^c$-manifolds with non-abelian Lie-group actions. We apply this result to study non-abelian symmetries of quasitoric manifolds. We give upper bounds for the degree of symmetry of these manifolds.