A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere
Geometric Topology
2026-04-20 v1
Abstract
For the genus- Heegaard surface in the -sphere, we present a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere for the surface. As a consequence, we reduce the connectivity problem in the reducing sphere complex for the surface to the problem of showing that any two vertices, whose representative reducing spheres are disjoint from a fixed non-separating compressing disk for the surface, are connected in the complex.
Cite
@article{arxiv.2604.15722,
title = {A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere},
author = {Sangbum Cho and Yuya Koda and Jung Hoon Lee},
journal= {arXiv preprint arXiv:2604.15722},
year = {2026}
}
Comments
17 pages, 6 figures