7 citations · 30 across the 38 of their papers we have counts for
38 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…
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…
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…
Divides and hyperbolic volumes
Ryoga Furutani, Yuya Koda
A divide is the image of a proper and generic immersion of a compact -manifold into the -disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere.…
Positive flow-spines and contact 3-manifolds, II
Ippei Ishii, Masaharu Ishikawa, Yuya Koda +1
This paper corresponds to Section 8 of arXiv:1912.05774v3 [math.GT]. The contents until Section 7 are published in Annali di Matematica Pura ed Applicata as a separate paper. In th…
Handlebody decompositions of 3-manifolds and polycontinuous patterns
Naoki Sakata, Ryosuke Mishina, Masaki Ogawa +4
We introduce the concept of a handlebody decomposition of a 3-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a c…
Presentation of the fundamental groups of complements of shadows
Masaharu Ishikawa, Yuya Koda, Hironobu Naoe
A shadowed polyhedron is a simple polyhedron equipped with half integers on regions, called gleams, which represents a compact, oriented, smooth 4-manifold. The polyhedron is embed…
Distance and the Goeritz groups of bridge decompositions
Daiki Iguchi, Yuya Koda
We prove that if the distance of a bridge decomposition of a link with respect to a Heegaard splitting of a -manifold is at least , then the Goeritz group is a finite group.
Stable maps and hyperbolic links
Ryoga Furutani, Yuya Koda
A stable map of a closed orientable -manifold into the real plane is called a stable map of a link in the manifold if the link is contained in the set of definite fold points. W…
Homotopy motions of surfaces in -manifolds
Yuya Koda, Makoto Sakuma
We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion a…
Goeritz groups of bridge decompositions
Susumu Hirose, Daiki Iguchi, Eiko Kin +1
For a bridge decomposition of a link in the -sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the -sphere th…
Positive flow-spines and contact 3-manifolds
Ippei Ishii, Masaharu Ishikawa, Yuya Koda +1
A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an op…
Twisted book decompositions and the Goeritz groups
Daiki Iguchi, Yuya Koda
We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance that have the infin…
Shadows of acyclic 4-manifolds with sphere boundary
Yuya Koda, Hironobu Naoe
In terms of Turaev's shadows, we provide a sufficient condition for a compact, smooth, acyclic 4-manifold with boundary the 3-sphere to be diffeomorphic to the standard 4-ball. As…
Braid group and leveling of a knot
Sangbum Cho, Yuya Koda, Arim Seo
Any knot in genus- -bridge position can be moved by isotopy to lie in a union of parallel tori tubed by tubes so that intersects each tube in two spanning a…
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.…
Neighborhood equivalence for multibranched surfaces in 3-manifolds
Kai Ishihara, Yuya Koda, Makoto Ozawa +1
A multibranched surface is a 2-dimensional polyhedron without vertices. We introduce moves for multibranched surfaces embedded in a 3-manifold, which connect any two multibranched…
Extending automorphisms of the genus-2 surface over the 3-sphere
Kenta Funayoshi, Yuya Koda
An automorphism of a closed orientable surface is said to be extendable over the 3-sphere if extends to an automorphism of the pair with respect to som…