Topology of $3$-manifolds with uniformly positive scalar curvature
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911019782111232 |
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| author | Wang, Jian |
| author_facet | Wang, Jian |
| contents | In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is homeomorphic to an (possibly) infinite connected sum of spherical $3$-manifolds and some copies of $\mathbb{S}^1\times \mathbb{S}^2$. Further, we study an oriented $3$-manifold with mean convex boundary and with uniformly positive scalar curvature. If the boundary is a disjoint union of closed surfaces, then the manifold is an (possibly) infinite conned sum of spherical $3$-manifolds, some handlebodies and some copies of $\mathbb{S}^1\times \mathbb{S}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14383 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Topology of $3$-manifolds with uniformly positive scalar curvature Wang, Jian Differential Geometry Geometric Topology In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is homeomorphic to an (possibly) infinite connected sum of spherical $3$-manifolds and some copies of $\mathbb{S}^1\times \mathbb{S}^2$. Further, we study an oriented $3$-manifold with mean convex boundary and with uniformly positive scalar curvature. If the boundary is a disjoint union of closed surfaces, then the manifold is an (possibly) infinite conned sum of spherical $3$-manifolds, some handlebodies and some copies of $\mathbb{S}^1\times \mathbb{S}^2$. |
| title | Topology of $3$-manifolds with uniformly positive scalar curvature |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2212.14383 |