A note on the topology of Lefschetz fibrations
Geometric Topology
2025-10-06 v1
Abstract
We prove an upper bound for the first Betti number of a nontrivial genus- 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.
Cite
@article{arxiv.2510.03173,
title = {A note on the topology of Lefschetz fibrations},
author = {Sierra Knavel},
journal= {arXiv preprint arXiv:2510.03173},
year = {2025}
}