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2020 Positive scalar curvature metrics via end-periodic manifolds
Michael Hallam, Varghese Mathai
Ann. K-Theory 5(3): 639-676 (2020). DOI: 10.2140/akt.2020.5.639

Abstract

We obtain two types of results on positive scalar curvature metrics for compact spin manifolds that are even-dimensional. The first type of result are obstructions to the existence of positive scalar curvature metrics on such manifolds, expressed in terms of end-periodic eta invariants that were defined by Mrowka, Ruberman and Saveliev (Mrowka et al. 2016). These results are the even-dimensional analogs of the results by Higson and Roe (2010). The second type of result studies the number of path components of the space of positive scalar curvature metrics modulo diffeomorphism for compact spin manifolds that are even-dimensional, whenever this space is nonempty. These extend and refine certain results in (Botvinnik and Gilkey 1995) and also (Mrowka et al. 2016). End-periodic analogs of K-homology and bordism theory are defined and are utilised to prove many of our results.

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Michael Hallam. Varghese Mathai. "Positive scalar curvature metrics via end-periodic manifolds." Ann. K-Theory 5 (3) 639 - 676, 2020. https://doi.org/10.2140/akt.2020.5.639

Information

Received: 18 February 2019; Revised: 8 January 2020; Accepted: 26 January 2020; Published: 2020
First available in Project Euclid: 11 August 2020

zbMATH: 07237245
MathSciNet: MR4132750
Digital Object Identifier: 10.2140/akt.2020.5.639

Subjects:
Primary: 58J28
Secondary: 19K33 , 19K56 , 53C21

Keywords: end-periodic bordism , end-periodic eta invariant , end-periodic K-homology , end-periodic manifolds , maximal Baum–Connes conjecture , positive scalar curvature metrics , vanishing theorems

Rights: Copyright © 2020 Mathematical Sciences Publishers

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