Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere
Geometric Topology
2025-09-30 v1
Abstract
Given a Heegaard surface in the -sphere, we show that any non-separating weak reducing pair for the surface admits a reducing sphere that separates the two disks of the pair if and only if the genus of the surface is at most .
Keywords
Cite
@article{arxiv.2509.24388,
title = {Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere},
author = {Sangbum Cho and Yuya Koda and Jung Hoon Lee},
journal= {arXiv preprint arXiv:2509.24388},
year = {2025}
}
Comments
6 pages, 2 figures