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 $3$.

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