8 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 symmetry and exterior problems of knotted handlebodies
Yuya Koda, Makoto Ozawa, Yi-Sheng Wang
The paper concerns two classical problems in knot theory pertaining to knot symmetry and knot exteriors. In the context of a knotted handlebody in a -sphere , the symme…
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 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…
Quantum enhancement polynomials associated with the canonical two-element tricbracket
Yuya Koda, Yuya Nishimura, Yuka Sakamoto
Quantum enhancement polynomials are invariants for oriented links, defined in association with an algebraic structure called a tribracket. In this paper, we focus on the particular…