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|Title:||Positive scalar curvature and callias-type index theorems for proper actions|
|Citation:||Bulletin of the Australian Mathematical Society, 2019; 99(2):342-343|
|Publisher:||Cambridge University Press (CUP)|
|Hao Guo, Peter Hochs and Varghese Mathai|
|Abstract:||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 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 G-invariant Riemannian metrics with uniformly positive scalar curvature, under an equivariant bounded geometry assumption.|
|Keywords:||Callias operator; index; positive scalar curvature; proper group action|
|Rights:||© Copyright 2021 Mathematical Sciences Publishers. All rights reserved.|
|Appears in Collections:||Aurora harvest 4|
Mathematical Sciences publications
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