4 papers
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…
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…
On the Invalidity of Lemma 2.5 in our previous work on the Powell Conjecture
Sangbum Cho, Yuya Koda, Jung Hoon Lee +1
In our previous version entitled ``The reducing sphere complexes for the 3-sphere are connected: a proof of the Powell Conjecture", we claimed to prove the Powell Conjecture, which…
The Powell Conjecture for the genus-three Heegaard splitting of the -sphere
Sangbum Cho, Yuya Koda, Jung Hoon Lee
The Powell Conjecture states that the Goeritz group of the Heegaard splitting of the -sphere is finitely generated; furthermore, four specific elements suffice to generate the g…