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https://hdl.handle.net/2440/130023
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Type: | Journal article |
Title: | Equivariant Callias index theory via coarse geometry |
Author: | Guo, H. Hochs, P. Mathai, V. |
Citation: | Annales de l'Institut Fourier, 2021; 71(6):2387-2430 |
Publisher: | Association des Annales de l'Institut Fourier |
Issue Date: | 2021 |
ISSN: | 0373-0956 1777-5310 |
Statement of Responsibility: | Hao Guo, Peter Hochs, Varghese Mathai |
Abstract: | The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over C*-algebras of continuous functions to obtain a meaningful index. Inspired by work by Roe, we then develop a localised variant, with values in the K-theory of a group C*-algebra. This generalises the Baum-Connes assembly map to non-cocompact actions. We show that an equivariant index for Callias-type operators is a special case of this localised index, obtain results on existence and non-existence of Riemannian metrics of positive scalar curvature invariant under proper group actions, and show that a localised version of the Baum-Connes conjecture is weaker than the original conjecture, while still giving a conceptual description of the K-theory of a group C*-algebra. |
Description: | Published 21 Apr 2021 |
Rights: | © Association des Annales de l’institut Fourier, 2021. Article mis à disposition par ses auteurs selon les termes de la licence Creative Commons attribution – pas de modification 3.0 France http://creativecommons.org/licenses/by-nd/3.0/fr/ |
DOI: | 10.5802/aif.3445 |
Grant ID: | http://purl.org/au-research/grants/arc/FL170100020 http://purl.org/au-research/grants/arc/DP200100729 |
Published version: | https://aif.centre-mersenne.org/ |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
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hdl_130023.pdf | Published version | 1.51 MB | Adobe PDF | View/Open |
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