We establish a vanishing result for indices of certain twisted Dirac operators on –manifolds with nonabelian Lie group actions. We apply this result to study nonabelian symmetries of quasitoric manifolds. We give upper bounds for the degree of symmetry of these manifolds.
Michael Wiemeler. "Dirac operators and symmetries of quasitoric manifolds." Algebr. Geom. Topol. 13 (1) 277 - 312, 2013. https://doi.org/10.2140/agt.2013.13.277