Positive scalar curvature and exotic structures on simply connected four manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866910800933814272 |
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| author | Kumar, Aditya Sen, Balarka |
| author_facet | Kumar, Aditya Sen, Balarka |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive scalar curvature and exotic structures on simply connected four manifolds Kumar, Aditya Sen, Balarka Differential Geometry Geometric Topology 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. |
| title | Positive scalar curvature and exotic structures on simply connected four manifolds |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2501.01113 |