Complete Riemannian 4-manifolds with uniformly positive scalar curvature
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910517589704704 |
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| author | Chodosh, Otis Maximo, Davi Mukherjee, Anubhav |
| author_facet | Chodosh, Otis Maximo, Davi Mukherjee, Anubhav |
| contents | We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) $4$-manifolds. In particular, such a metric on the interior of a compact contractible $4$-manifold uniquely distinguishes the standard $4$-ball up to diffeomorphism among Mazur manifolds and up to homeomorphism in general.
We additionally show there exist uncountably many exotic $\mathbb{R}^4$'s that do not admit such a metric and that any (non-compact) tame $4$-manifold has a smooth structure that does not admit such a metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete Riemannian 4-manifolds with uniformly positive scalar curvature Chodosh, Otis Maximo, Davi Mukherjee, Anubhav Differential Geometry Geometric Topology Symplectic Geometry We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) $4$-manifolds. In particular, such a metric on the interior of a compact contractible $4$-manifold uniquely distinguishes the standard $4$-ball up to diffeomorphism among Mazur manifolds and up to homeomorphism in general. We additionally show there exist uncountably many exotic $\mathbb{R}^4$'s that do not admit such a metric and that any (non-compact) tame $4$-manifold has a smooth structure that does not admit such a metric. |
| title | Complete Riemannian 4-manifolds with uniformly positive scalar curvature |
| topic | Differential Geometry Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2407.05574 |