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arXiv · 2509.24388

Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere

Sangbum Cho·Yuya Koda·Jung Hoon Lee
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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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Sangbum Cho, Yuya Koda, Jung Hoon Lee. 2025-09-29. Reducing spheres and weak reducing pairs for Heegaard surfaces in the $3$-sphere. https://arxiv.org/abs/2509.24388

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