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

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Authors
Burkemper, Matthew Bryan
Searle, Catherine
Walsh, Mark
Advisors
Issue Date
2022-11-01
Type
Preprint
Keywords
Positive -intermediate scalar curvature , Surgery and cobordism , Isotopy and concordance , Moduli spaces of Riemannian metrics
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Citation
Burkemper, M., Searle, C., & Walsh, M. (2022). Positive (p,n)-intermediate scalar curvature and cobordism. Journal of Geometry and Physics, 181, 104625. https://doi.org/https://doi.org/10.1016/j.geomphys.2022.104625
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 (,)-intermediate scalar curvature for 0≤−2 for surgeries in codimension at least +3. We then use it to generalize a well known theorem of Carr. Letting () denote the space of positive (,)-intermediate scalar curvature metrics on an n-manifold , we show for 0 ≤ p ≤ 2−3 and ≥ 2, that for a closed, spin, (4−1)-manifold M admitting a metric of positive (, 4−1)-intermediate scalar curvature, Extra open brace or missing close braceR^{sp,n>0,4n−1^>0}($$M$) has infinitely many path components.

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Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article.
Publisher
Elsevier
Journal
Book Title
Series
Journal of Geometry and Physics
Volume 181
PubMed ID
DOI
ISSN
0393-0440
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