On sections of maps from 4-manifolds to the 2-sphere
Geometric Topology
2025-06-24 v1
Abstract
This note exhibits singular fibrations over the 2-sphere whose regular fibers are connected surfaces of arbitrarily high genus, but which admit no sections. These include achiral Lefschetz fibrations, as well as generic maps for which some disks cannot lift to sections -- in fact, neither hemisphere lifts.
Keywords
Cite
@article{arxiv.2506.18066,
title = {On sections of maps from 4-manifolds to the 2-sphere},
author = {Robert E. Gompf},
journal= {arXiv preprint arXiv:2506.18066},
year = {2025}
}
Comments
4 pages, 1 figure