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math.GT2024
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…
math.GT2024
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…
math.GT2024
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…