Abstract
For a proper action by a locally compact group on a manifold with a -equivariant -structure, we obtain obstructions to the existence of complete -invariant Riemannian metrics with uniformly positive scalar curvature. We focus on the case where is noncompact. The obstructions follow from a Callias-type index theorem, and relate to positive scalar curvature near hypersurfaces in . We also deduce some other applications of this index theorem. If is a connected Lie group, then the obstructions to positive scalar curvature vanish under a mild assumption on the action. In that case, we generalise a construction by Lawson and Yau to obtain complete -invariant Riemannian metrics with uniformly positive scalar curvature, under an equivariant bounded geometry assumption.
Citation
Hao Guo. Peter Hochs. Varghese Mathai. "Positive scalar curvature and an equivariant Callias-type index theorem for proper actions." Ann. K-Theory 6 (2) 319 - 356, 2021. https://doi.org/10.2140/akt.2021.6.319
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