Dodecahedral L-spaces and hyperbolic 4-manifolds
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910754330902528 |
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| author | Battista, Ludovico Ferrari, Leonardo Santoro, Diego |
| author_facet | Battista, Ludovico Ferrari, Leonardo Santoro, Diego |
| contents | We prove that exactly 6 out of the 29 rational homology 3-spheres tessellated by four or less right-angled hyperbolic dodecahedra are L-spaces. The algorithm used is based on the L-space census provided by Dunfield in arXiv:1904.04628, and relies on a result by Rasmussen-Rasmussen arXiv:1508.05900. We use the existence of these manifolds together with a result of Martelli arXiv:1510.06325 to construct explicit examples of hyperbolic 4-manifolds containing separating L-spaces, and therefore having vanishing Seiberg-Witten invariants. This answers a question asked by Agol and Lin in arXiv:1812.06536. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_01542 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dodecahedral L-spaces and hyperbolic 4-manifolds Battista, Ludovico Ferrari, Leonardo Santoro, Diego Geometric Topology We prove that exactly 6 out of the 29 rational homology 3-spheres tessellated by four or less right-angled hyperbolic dodecahedra are L-spaces. The algorithm used is based on the L-space census provided by Dunfield in arXiv:1904.04628, and relies on a result by Rasmussen-Rasmussen arXiv:1508.05900. We use the existence of these manifolds together with a result of Martelli arXiv:1510.06325 to construct explicit examples of hyperbolic 4-manifolds containing separating L-spaces, and therefore having vanishing Seiberg-Witten invariants. This answers a question asked by Agol and Lin in arXiv:1812.06536. |
| title | Dodecahedral L-spaces and hyperbolic 4-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2208.01542 |