Burkemper, Matthew and Searle, Catherine and Walsh, Mark G. (2022) Positive (p,n)-intermediate scalar curvature and cobordism. Journal of Geometry and Physics, 181 (104625). pp. 1-28. ISSN 0393-0440

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Abstract

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 extend this construction for (p,n)-intermediate scalar curvature for 0≤p≤n−2 for surgeries in codimension at least p + 3. We then use it to generalize a well known theorem of Carr. Letting Rsp,n>0(M) denote the space of positive (p,n)-intermediate scalar curvature metrics on an n-manifold M, we show for 0≤p≤2n−3 and n ≥ 2, that for a closed, spin, (4n − 1)-manifold M admitting a metric of positive (p, 4n − 1)-intermediate scalar curvature, Rsp,4n−1>0(M) has infinitely many path components.

Item Type:	Article
Keywords:	Positive; (p,n); -intermediate scalar curvature; Surgery and cobordism; Isotopy and concordance; Moduli spaces of Riemannian metrics;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	18288
Identification Number:	https://doi.org/10.1016/j.geomphys.2022.104625
Depositing User:	Mark Walsh
Date Deposited:	19 Mar 2024 15:57
Journal or Publication Title:	Journal of Geometry and Physics
Publisher:	Elsevier
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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