A note on the topology of Lefschetz fibrations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911190917054464 |
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| author | Knavel, Sierra |
| author_facet | Knavel, Sierra |
| contents | We prove an upper bound for the first Betti number of a nontrivial genus-$g$ Lefschetz fibration. We also show that if the monodromy of a Lefschetz fibration is transitive with respect to the mapping class group, the Lefschetz fibration is simply connected. Lastly, we discuss a potential family of indecomposable genus-2 Lefschetz fibrations with maximally non-trivial first homology which would be candidates for large fundamental group computations, if they exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the topology of Lefschetz fibrations Knavel, Sierra Geometric Topology We prove an upper bound for the first Betti number of a nontrivial genus-$g$ Lefschetz fibration. We also show that if the monodromy of a Lefschetz fibration is transitive with respect to the mapping class group, the Lefschetz fibration is simply connected. Lastly, we discuss a potential family of indecomposable genus-2 Lefschetz fibrations with maximally non-trivial first homology which would be candidates for large fundamental group computations, if they exist. |
| title | A note on the topology of Lefschetz fibrations |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2510.03173 |