On the space of riemannian metrics satisfying surgery stable curvature conditions

Kordaß, Jan-Bernhard

doi:10.48550/arxiv.1808.00581

Cited by 3 publications

(6 citation statements)

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“…More recently, Kordass [22], proved this fact for a variety of general curvature conditions including positive pp, nq-intermediate scalar curvature. In particular, Theorem 3.1 from [22], which we state below, is a special case of his results. Lemma 6.2 ( [22]).…”

Section: 5mentioning

confidence: 88%

“…In particular, Theorem 3.1 from [22], which we state below, is a special case of his results. Lemma 6.2 ( [22]). Let M be a smooth n-dimensional manifold and let φ : S k ˆD `1 Ñ M be an embedding with k` `1 " n, ě 2 and p P t0, 1, ¨¨¨, ´2u.…”

Section: 5mentioning

confidence: 88%

“…Proofs of this fact for the case of positive scalar curvature, that is when p " 0, can be found in Theorem 2.3 of [35] and in [10]. More recently, Kordass [22], proved this fact for a variety of general curvature conditions including positive pp, nq-intermediate scalar curvature. In particular, Theorem 3.1 from [22], which we state below, is a special case of his results.…”

Section: 5mentioning

confidence: 90%

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Positive $(p, n)$-intermediate scalar curvature and cobordism

Burkemper,

Searle,

Walsh

2021

Preprint

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In this paper we consider a well-known construction due to Gromov and Lawson, Schoen and Yau, Gajer, and Walsh which allows for the extension of a metric of positive scalar curvature over the trace of a surgery in codimension at least 3 to a metric of positive scalar curvature which is a product near the boundary. We generalize this construction to work for pp, nq-intermediate scalar curvature for 0 ď p ď n ´2 for surgeries in codimension at least p`3. We then use it to generalize a well known theorem of Carr. Letting R sp,ną0 pM q denote the space of positive pp, nq-intermediate scalar curvature metrics on an n-manifold M , we show for 0 ď p ď 2n ´3 and n ě 2, that for a closed, spin, p4n ´1q-manifold M admitting a metric of positive pp, 4n ´1q-intermediate scalar curvature, R s p,4n´1 ą0 pM q has infinitely many path components.

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Section: 5mentioning

confidence: 88%

Section: 5mentioning

confidence: 88%

Section: 5mentioning

confidence: 90%

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Positive $(p, n)$-intermediate scalar curvature and cobordism

Burkemper,

Searle,

Walsh

2021

Preprint

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“…max{3, d−k+2}) surgery-stable on d-manifolds for d ≥ 3. By work of the second named author [Kor20] these conditions are in fact parametrized surgery-stable with the same codimension restriction. (3) The condition sec < 0 gives rise to a Riemannian functor, which is codimension 2 surgery stable on 2-manifolds.…”

Section: All Of the Above Examples Are Given By Open Convex Conesmentioning

confidence: 99%

Spaces of positive intermediate curvature metrics

Frenck,

Kordaß

2020

Preprint

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“…Then there is the notion of k -positive curvature (also known in the literature as the k th -intermediate Ricci curvature or k th -Ricci curvature), see for example [15], [28], [29], [36], [33], [14], [11], [12], [13] [23], [24]. We take special note of the paper [18], which concerns the topology of the space of metrics satisfying so-called 'surgery stable' curvature conditions, building on ideas developed in [17]. This includes positive scalar curvature, as well as a number of other conditions.…”

Section: Introductionmentioning

confidence: 99%

H-Space and Loop Space Structures for Intermediate Curvatures

Walsh¹,

Wraith²

2020

Preprint

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For dimensions n ≥ 3 and k ∈ {2, • • • , n}, we show that the space of metrics of k -positive Ricci curvature on the sphere S n has the structure of an H -space with a homotopy commutative, homotopy associative product operation. We further show, using the theory of operads and results of Boardman, Vogt and May that the path component of this space containing the round metric is weakly homotopy equivalent to an n -fold loop space.

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On the space of riemannian metrics satisfying surgery stable curvature conditions

Cited by 3 publications

References 0 publications

Positive $(p, n)$-intermediate scalar curvature and cobordism

Positive $(p, n)$-intermediate scalar curvature and cobordism

Spaces of positive intermediate curvature metrics

H-Space and Loop Space Structures for Intermediate Curvatures

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