On the space of riemannian metrics satisfying surgery stable curvature conditions

Kordaß, Jan-Bernhard

doi:10.1007/s00208-023-02563-4

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Remark 28 (I)1

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2023

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Cited by 2 publications

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“…is a weak homotopy equivalence. (ii) A parametrised version of the surgery theorem has been proven by Chernysh [4] (see also [9,22]). In its general form, it states that for k ≥ 3 the metric g N + g tor is a right-stable metric on N × D k , g tor a torpedo metric 5 and g N any metric on N such that g N + g tor has positive scalar curvature.…”

Section: Remark 28 (I)mentioning

confidence: 99%

Spaces of positive scalar curvature metrics on totally nonspin manifolds with spin boundary

Frenck

2023

Math. Z.

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In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, those spaces are not connected and have nontrivial fundamental group. Furthermore we show that a well-known propagation technique for detection results on spaces of positive scalar curvature metrics on spin manifolds ceases to work in the totally nonspin case.

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Section: Remark 28 (I)mentioning

confidence: 99%

Spaces of positive scalar curvature metrics on totally nonspin manifolds with spin boundary

Frenck

2023

Math. Z.

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On the homotopy type of the space of metrics of positive scalar curvature

Ebert

Wiemeler

2023

J. Eur. Math. Soc.

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Let M^d be a simply connected spin manifold of dimension d \geq 5 admitting Riemannian metrics of positive scalar curvature. Denote by \mathcal{R}^+(M^d) the space of such metrics on M^d . We show that \mathcal{R}^+(M^d) is homotopy equivalent to \mathcal{R}^+(S^d) , where S^d denotes the d -dimensional sphere with standard smooth structure. We also show a similar result for simply connected non-spin manifolds M^d with d\geq 5 and d\neq 8 . In this case let W^d be the total space of the non-trivial S^{d-2} -bundle with structure group SO(d-1) over S^2 . Then \mathcal{R}^+(M^d) is homotopy equivalent to \mathcal{R}^+(W^d) .

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On the space of riemannian metrics satisfying surgery stable curvature conditions

Cited by 2 publications

References 28 publications

Spaces of positive scalar curvature metrics on totally nonspin manifolds with spin boundary

Spaces of positive scalar curvature metrics on totally nonspin manifolds with spin boundary

On the homotopy type of the space of metrics of positive scalar curvature

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