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https://hdl.handle.net/2440/131643
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Type: | Journal article |
Title: | Positive scalar curvature and callias-type index theorems for proper actions |
Author: | Guo, H. Hochs, P. Varghese, M. |
Citation: | Bulletin of the Australian Mathematical Society, 2019; 99(2):342-343 |
Publisher: | Cambridge University Press (CUP) |
Issue Date: | 2019 |
ISSN: | 0004-9727 1755-1633 |
Statement of Responsibility: | 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. |
DOI: | 10.1017/S0004972718001338 |
Grant ID: | http://purl.org/au-research/grants/arc/DP200100729 |
Published version: | http://dx.doi.org/10.2140/akt.2021.6.319 |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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