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Abstract
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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
-homology
and bordism theory are defined and are utilised to prove many of our results.
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Keywords
positive scalar curvature metrics, maximal Baum–Connes
conjecture, end-periodic manifolds, end-periodic
K-homology, end-periodic eta invariant, vanishing theorems,
end-periodic bordism
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Mathematical Subject Classification 2010
Primary: 58J28
Secondary: 19K33, 19K56, 53C21
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Milestones
Received: 18 February 2019
Revised: 8 January 2020
Accepted: 26 January 2020
Published: 28 July 2020
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