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Article overview
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Positive $(p, n)$-intermediate scalar curvature and cobordism | Matthew Burkemper
; Catherine Searle
; Mark Walsh
; | Date: |
22 Oct 2021 | 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 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 | Services: | Forum | Review | PDF | Favorites |
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