Loading...
Positive (p,n)-intermediate scalar curvature and cobordism
Burkemper, Matthew Bryan Searle, Catherine Walsh, Mark
Burkemper, Matthew Bryan
Searle, Catherine
Walsh, Mark
Citations
Altmetric:
Files
Loading...
Preprint
Adobe PDF, 677.69 KB
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2022-11-01
Type
Preprint
Genre
Keywords
Positive -intermediate scalar curvature,Surgery and cobordism,Isotopy and concordance,Moduli spaces of Riemannian metrics
Subjects (LCSH)
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 ($p$,$n$)-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 $R^{sp,n>0}$($M$) denote the space of positive ($p$,$n$)-intermediate scalar curvature metrics on an n-manifold $M$, we show for 0 ≤ p ≤ 2$n$−3 and $n$ ≥ 2, that for a closed, spin, (4$n$−1)-manifold M admitting a metric of positive ($p$, 4$n$−1)-intermediate scalar curvature, $R^{sp,n>0$,4n−1^>0}($$M$) has infinitely many path components.
Table of Contents
Description
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
Volume 181
Digital Collection
Finding Aid URL
Use and Reproduction
Archival Collection
PubMed ID
DOI
ISSN
0393-0440