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Lefschetz fibrations with handlebody monodromy
Abstract
We study relatively minimal Lefschetz fibrations over closed oriented surfaces whose monodromy extends over a fixed 3--dimensional handlebody. If X is the total space and ℓ is the number of critical points, we prove that σ(X)=−ℓ. Such fibrations with ℓ>0 exist precisely for fiber genus g≥3 and base genus h≥2, and one can take ℓ=1 for every such pair. We also show that hyperelliptic handlebody monodromy forces the fibration to be a surface bundle and that every meridian twist, separating or nonseparating, has commutator length two in the handlebody group for g≥3.
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BibTeX
@misc{baykur2026lefschetz,
title = {{Lefschetz fibrations with handlebody monodromy}},
author = {R. Inanc Baykur and Susumu Hirose},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05537},
eprint = {2610.05537},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05537},
}
RIS
TY - UNPB
TI - Lefschetz fibrations with handlebody monodromy
AU - R. Inanc Baykur
AU - Susumu Hirose
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05537
UR - https://arxiv.org/abs/2610.05537
AB - We study relatively minimal Lefschetz fibrations over closed oriented surfaces whose monodromy extends over a fixed 3--dimensional handlebody. If X is the total space and ℓ is the number of critical points, we prove that σ(X)=−ℓ. Such fibrations with ℓ>0 exist precisely for fiber genus g≥3 and base genus h≥2, and one can take ℓ=1 for every such pair. We also show that hyperelliptic handlebody monodromy forces the fibration to be a surface bundle and that every meridian twist, separating or nonseparating, has commutator length two in the handlebody group for g≥3.
ER -