5 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…
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…
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…