7 citations · 30 across the 38 of their papers we have counts for
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…
Essential annuli in genus two handlebody exteriors
Yuya Koda, Makoto Ozawa, Yi-Sheng Wang
We classify all potential configurations of essential annuli in a genus two atoroidal handlebody exterior in the -sphere, building on two recent classifications: the classificat…
The Goeritz groups of -decompositions
Yuya Koda, Yuki Tanaka
A -decomposition of a link in a closed orientable -manifold is a decomposition of by a closed orientable surface of genus into two handebodies each inter…
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…
Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups
Yuya Koda, Kazuto Takao
We give two criteria for diagrams of Heegaard splittings of 3-manifolds. Weaker one of them guarantees that the splitting is strongly irreducible, and the stronger one guarantees i…