5 citations · 8 across the 15 of their papers we have counts for
16 papers
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…
Note on primitive disk complexes
Sangbum Cho, Jung Hoon Lee
Given a Heegaard splitting of the -sphere, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting. It i…
Linearly Free Graphs
Youngsik Huh, Jung Hoon Lee
In this paper we are interested in an intrinsic property of graphs which is derived from their embeddings into the Euclidean 3-space . An embedding of a graph into $\…
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.…
Bridge surfaces with the topological minimality preserved by perturbation
Jung Hoon Lee
We show that except for if a bridge surface for a knot is an index topologically minimal surface, then after a perturbation it is still topologically minimal with index…
Bridge spheres for the unknot are topologically minimal
Jung Hoon Lee
We show that an -bridge sphere for the unknot is a topologically minimal surface of index at most .
Linearly embedded graphs in 3-space with homotopically free exteriors
Youngsik Huh, Jung Hoon Lee
An embedding of a graph into is said to be linear, if any edge of the graph is sent to be a line segment. And we say that an embedding of a graph into $\math…
On the connectedness of subcomplexes of a disk complex
Jung Hoon Lee
For a boundary-reducible -manifold with a genus surface, we show that if admits a genus Heegaard surface , then the disk complex of is simp…
Critical Heegaard surfaces obtained by amalgamation
Jung Hoon Lee
Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition…
Rectangle condition for compression body and 2-fold branched covering
Jungsoo Kim, Jung Hoon Lee
We give the rectangle condition for strong irreducibility of Heegaard splittings of -manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a $2…
Examples of unstabilized critical Heegaard surfaces
Jung Hoon Lee
We show that the standard minimal genus Heegaard splitting of (closed orientable surface)\times S^1 is a critical Heegaard splitting.
Twisted torus knots T(p,q,3,s) are tunnel number one
Jung Hoon Lee
We show that twisted torus knots are tunnel number one. A short spanning arc connecting two adjacent twisted strands is an unknotting tunnel.
Parity criterion and Dehn twists for unstabilized Heegaard splittings
Jung Hoon Lee
We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application, we construct unstabilized Heegaard splittings…