Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/130320
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Type: | Journal article |
Title: | Coarse geometry and Callias quantisation |
Author: | Guo, H. Hochs, P. Mathai, V. |
Citation: | Transactions of the American Mathematical Society, 2021; 374(4):2479-2520 |
Publisher: | American Mathematical Society |
Issue Date: | 2021 |
ISSN: | 0002-9947 1088-6850 |
Statement of Responsibility: | Hao Guo, Peter Hochs and Varghese Mathai |
Abstract: | Consider a proper, isometric action by a unimodular, locally compact group G on a complete Riemannian manifold M. For equivariant elliptic operators that are invertible outside a cocompact subset of M, we show that a localised index in the K-theory of the maximal group C∗-algebra of G is welldefined. The approach is based on the use of maximal versions of equivariant localised Roe algebras, and many of the technical arguments in this paper are used to handle the ways in which they differ from their reduced versions. By using the maximal group C∗-algebra instead of its reduced counterpart, we can apply the trace given by integration over G to recover an index defined earlier by the last two authors, and developed further by Braverman, in terms of sections invariant under the group action. This leads to refinements of index-theoretic obstructions to Riemannian metrics of positive scalar curvature on noncompact manifolds, and also on orbifolds and other singular quotients of proper group actions. As a motivating application in another direction, we prove a version of Guillemin and Sternberg’s quantisation commutes with reduction principle for equivariant indices of Spinc Callias-type operators. |
Description: | Article electronically published on January 26, 2021 |
Rights: | © 2021 American Mathematical Society |
DOI: | 10.1090/tran/8202 |
Grant ID: | http://purl.org/au-research/grants/arc/FL170100020 |
Published version: | https://www.ams.org/publications/journals/journalsframework/tran |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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hdl_130320.pdf | Submitted version | 637.45 kB | Adobe PDF | View/Open |
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