Positive scalar curvature and exotic structures on simply connected four manifolds
Differential Geometry
2025-01-28 v2 Geometric Topology
Abstract
We address Gromov's band width inequality and Rosenberg's -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.
Keywords
Cite
@article{arxiv.2501.01113,
title = {Positive scalar curvature and exotic structures on simply connected four manifolds},
author = {Aditya Kumar and Balarka Sen},
journal= {arXiv preprint arXiv:2501.01113},
year = {2025}
}
Comments
v2. 19 pages. Substantially revised: Corrected lemmas and significantly simplified proofs in Section 3, added a new result for non-simply connected 4-manifolds. Minor improvements in exposition