If X×S¹ admits a PSC metric whose circle factor is at angle < 45° to the X-slice, then X itself admits a PSC metric, for any closed oriented X of dimension at least two.
Positive scalar curvature and exotic structures on simply connected four manifolds
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We address Gromov's band width inequality and Rosenberg's $S^1$-stability conjecture for simply connected smooth four manifolds. Both results are known to be false in dimension 4 due to counterexamples based on Seiberg-Witten invariants. Nevertheless we show that both of these results hold upon considering simply connected smooth four manifolds up to homeomorphism. We also obtain a related result for non-simply connected smooth four manifolds.
citation-role summary
background 1
citation-polarity summary
fields
math.DG 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
A Codimension Two Approach to the $\mathbb{S}^1$-Stability Conjecture
If X×S¹ admits a PSC metric whose circle factor is at angle < 45° to the X-slice, then X itself admits a PSC metric, for any closed oriented X of dimension at least two.