Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere
Sangbum Cho, Yuya Koda, Jung Hoon Lee
公開日: 2025/9/29
Abstract
Given a Heegaard surface in the $3$-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 $3$.