5 papers · 1 filter
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…
The primitive curve complex for a handlebody
Sangbum Cho, Jung Hoon Lee
A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve tra…
Normal forms for rational 3-tangles
Bo-hyun Kwon, Jung Hoon Lee
In this paper, we define the \textit{normal form} of collections of disjoint three \textit{bridge arcs} for a given rational -tangle. We show that there is a sequence of \textit…
Disk surgery and the primitive disk complexes of the -sphere
Sangbum Cho, Yuya Koda, Jung Hoon Lee
Given a genus- Heegaard splitting of the -sphere with , we show that the primitive disk complex for the splitting is not weakly closed under disk surgery operation.…