A note on the topology of Lefschetz fibrations

Sierra Knavel

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arXiv · 2510.03173

A note on the topology of Lefschetz fibrations

Sierra Knavel

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Abstract

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.

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BibTeX RIS

Sierra Knavel. 2025-10-03. A note on the topology of Lefschetz fibrations. https://arxiv.org/abs/2510.03173

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