Corpus ID: 210838601

Positive scalar curvature and an equivariant Callias-type index theorem for proper actions

@article{Guo2020PositiveSC,
  title={Positive scalar curvature and an equivariant Callias-type index theorem for proper actions},
  author={H. Guo and P. Hochs and V. Mathai},
  journal={arXiv: Differential Geometry},
  year={2020}
}
For a proper action by a locally compact group $G$ on a manifold $M$ with a $G$-equivariant Spin-structure, we obtain obstructions to the existence of complete $G$-invariant Riemannian metrics with uniformly positive scalar curvature. We focus on the case where $M/G$ is noncompact. The obstructions follow from a Callias-type index theorem, and relate to positive scalar curvature near hypersurfaces in $M$. We also deduce some other applications of this index theorem. If $G$ is a connected Lie… Expand
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