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Bibliographic Details
Main Author: Knavel, Sierra
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.03173
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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