Desingularizing positive scalar curvature 4-manifolds
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866914961877368832 |
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| author | Kazaras, Demetre |
| author_facet | Kazaras, Demetre |
| contents | We show that the bordism group of closed 3-manifolds with positive scalar curvature (psc) metrics is trivial by explicit methods. Our constructions are derived from scalar-flat K{ä}hler ALE surfaces discovered by Lock-Viaclovsky. Next, we study psc 4-manifolds with metric singularities along points and embedded circles. Our psc null-bordisms are essential tools in a desingularization process developed by Li-Mantoulidis. This allows us to prove a non-existence result for singular psc metrics on enlargeable 4-manifolds with uniformly Euclidean geometry. As a consequence, we obtain a positive mass theorem for asymptotically flat 4-manifolds with non-negative scalar curvature and low regularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1905_05306 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Desingularizing positive scalar curvature 4-manifolds Kazaras, Demetre Differential Geometry Geometric Topology 53C21, 53D23, 53C80, 57R90 We show that the bordism group of closed 3-manifolds with positive scalar curvature (psc) metrics is trivial by explicit methods. Our constructions are derived from scalar-flat K{ä}hler ALE surfaces discovered by Lock-Viaclovsky. Next, we study psc 4-manifolds with metric singularities along points and embedded circles. Our psc null-bordisms are essential tools in a desingularization process developed by Li-Mantoulidis. This allows us to prove a non-existence result for singular psc metrics on enlargeable 4-manifolds with uniformly Euclidean geometry. As a consequence, we obtain a positive mass theorem for asymptotically flat 4-manifolds with non-negative scalar curvature and low regularity. |
| title | Desingularizing positive scalar curvature 4-manifolds |
| topic | Differential Geometry Geometric Topology 53C21, 53D23, 53C80, 57R90 |
| url | https://arxiv.org/abs/1905.05306 |