Collapsing and group growth as obstructions to Einstein metrics on some smooth 4-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910398592057344 |
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| author | Peruyero, Haydeé Contreras Suárez-Serrato, Pablo |
| author_facet | Peruyero, Haydeé Contreras Suárez-Serrato, Pablo |
| contents | We show that a combination of collapsing and excessive growth from the fundamental group impedes the existence of Einstein metrics on several families of smooth four-manifolds. These include infrasolvmanifolds whose fundamental group is not virtually nilpotent, most elliptic surfaces of zero Euler characteristic, geometrizable manifolds with hyperbolic factor geometries in their geometric decomposition, and higher graph four-manifolds without purely negatively curved pieces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_14380 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Collapsing and group growth as obstructions to Einstein metrics on some smooth 4-manifolds Peruyero, Haydeé Contreras Suárez-Serrato, Pablo Differential Geometry Group Theory Geometric Topology 53C25, 53C23, 57R57 We show that a combination of collapsing and excessive growth from the fundamental group impedes the existence of Einstein metrics on several families of smooth four-manifolds. These include infrasolvmanifolds whose fundamental group is not virtually nilpotent, most elliptic surfaces of zero Euler characteristic, geometrizable manifolds with hyperbolic factor geometries in their geometric decomposition, and higher graph four-manifolds without purely negatively curved pieces. |
| title | Collapsing and group growth as obstructions to Einstein metrics on some smooth 4-manifolds |
| topic | Differential Geometry Group Theory Geometric Topology 53C25, 53C23, 57R57 |
| url | https://arxiv.org/abs/2107.14380 |