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math.GT2026
A note on reducing spheres for the genus-4 Heegaard surface in the 3-sphere
Sangbum Cho, Yuya Koda, Jung Hoon Lee
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…
math.GT2025
Reducing spheres and weak reducing pairs for Heegaard surfaces in the -sphere
Sangbum Cho, Yuya Koda, Jung Hoon Lee
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…
math.GT2025
The rectangle condition does not detect the strong irreducibility
Bo-hyun Kwon, Sungmo Kang, Jung Hoon Lee
The rectangle condition for a genus Heegaard splitting of a 3-manifold, defined by Casson and Gordon, provides a sufficient criterion for the Heegaard splitting to be strongly…