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29 March 2024
 
  » arxiv » 2110.12069

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Positive $(p, n)$-intermediate scalar curvature and cobordism
Matthew Burkemper ; Catherine Searle ; Mark Walsh ;
Date 22 Oct 2021
AbstractIn 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 $(p,n)$-intermediate scalar curvature for $0leq pleq n-2$ for surgeries in codimension at least $p+3$. We then use it to generalize a well known theorem of Carr. Letting ${cal R}^{s_{p,n}>0}(M)$ denote the space of positive $(p, n)$-intermediate scalar curvature metrics on an $n$-manifold $M$, we show for $0leq pleq 2n-3$ and $ngeq 2$, that for a closed, spin, $(4n-1)$-manifold $M$ admitting a metric of positive $(p,4n-1)$-intermediate scalar curvature, ${cal R}^{s_{p,4n-1}>0}(M)$ has infinitely many path components.
Source arXiv, 2110.12069
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