21 citations · 46 across the 23 of their papers we have counts for
26 papers
A recipe for constructing non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups
Jan Kim, Tattybubu Arap kyzy, Donghi Lee
Very recently, Kim and Lee presented an example of a non-Hopfian relatively hyperbolic group with a Hopfian peripheral subgroup, demonstrating a counterexample to Osin's well-known…
A non-Hopfian relatively hyperbolic group with respect to a Hopfian subgroup
Jan Kim, Donghi Lee
We produce an example demonstrating that every finitely generated relatively hyperbolic group with respect to a collection of Hopfian subgroups need not be Hopfian. This answers a…
Classification of parabolic generating pairs of Kleinian groups with two parabolic generators
Shunsuke Aimi, Donghi Lee, Shunsuke Sakai +1
We give an alternative proof to Agol's classification of parabolic generating pairs of non-free Kleinian groups generated by two parabolic transformations. As an application, we gi…
Non-residually finite groups hyperbolic relative to residually finite subgroups
Jan Kim, Donghi Lee
Let and be integers such that and . We show that all Baumslag-Solitar groups are non-residually finite groups hyperbolic relative…
A family of two generator non-Hopfian groups
Donghi Lee, Makoto Sakuma
We construct -generator non-Hopfian groups , where each has a specific presentation $G_m=\langle a, b \, | \, u_{r_{m,0}}=u_{r_{m,1}}=u_{r_{m,2}}= \…
Parabolic generating pairs of genus-one 2-bridge knot groups
Donghi Lee, Makoto Sakuma
We show that any parabolic generating pair of a genus-one hyperbolic 2-bridge knot group is equivalent to the upper or lower meridian pair. As an application, we obtain a complete…
Simple loops on 2-bridge spheres in Heckoid orbifolds for the trivial knot
Donghi Lee, Makoto Sakuma
In this paper, we give a necessary and sufficient condition for an essential simple loop on a -bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopi…
Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (II)
Donghi Lee, Makoto Sakuma
In this paper and its prequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to b…
Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (I)
Donghi Lee, Makoto Sakuma
In this paper and its sequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be…
Simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links
Donghi Lee, Makoto Sakuma
Following Riley's work, for each 2-bridge link of slope $r\in\QQ$ and an integer or a half-integer greater than 1, we introduce the {\it Heckoid orbifold $\orbs(r;n)$} a…
Epimorphisms from 2-bridge link groups onto Heckoid groups (II)
Donghi Lee, Makoto Sakuma
In Part I of this series of papers, we made Riley's definition of Heckoid groups for 2-bridge links explicit, and gave a systematic construction of epimorphisms from 2-bridge link…
Epimorphisms from 2-bridge link groups onto Heckoid groups (I)
Donghi Lee, Makoto Sakuma
Riley "defined" the Heckoid groups for 2-bridge links as Kleinian groups, with nontrivial torsion, generated by two parabolic transformations, and he constructed an infinite family…
A new proof for small cancellation conditions of 2-bridge link groups
Daewa Kim, Donghi Lee
In this paper, we give a simple proof for the small cancellation conditions of the upper presentations of 2-bridge link groups, which holds the key to the proof of the main result…
A variation of McShane's identity for 2-bridge links
Donghi Lee, Makoto Sakuma
We give a variation of McShane's identity, which describes the cusp shape of a hyperbolic 2-bridge link in terms of the complex translation lengths of simple loops on the bridge sp…
Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (III)
Donghi Lee, Makoto Sakuma
This is the last of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homot…
Simple loops on 2-bridge spheres in 2-bridge link complements
Donghi Lee, Makoto Sakuma
The purpose of this note is to announce complete answers to the following questions. (1) For an essential simple loop on a 2-bridge sphere in a 2-bridge link complement, when is it…
Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II)
Donghi Lee, Makoto Sakuma
This is the second of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be hom…
Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (I)
Donghi Lee, Makoto Sakuma
In this paper and its two sequels, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in…
Epimorphisms between 2-bridge link groups: Homotopically trivial simple loops on 2-bridge spheres
Donghi Lee, Makoto Sakuma
We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we…
On several problems about automorphisms of the free group of rank two
Donghi Lee
Let be a free group of rank . In this paper we discuss three algorithmic problems related to automorphisms of . A word of is called positive if does not…
An algorithm that decides translation equivalence in a free group of rank two
Donghi Lee
Let F_2 be a free group of rank 2. We prove that there is an algorithm that decides whether or not, for given two elements u, v of F_2, u and v are translation equivalent in F_2, t…
Translation equivalent elements in free groups
Donghi Lee
Let F_n be a free group of rank n>1. Two elements g, h in F_n are said to be translation equivalent in F_n if the cyclic length of ϕ(g) equals the cyclic length of ϕ(h) for every a…
A tighter bound for the number of words of minimum length in an automorphic orbit
Donghi Lee
Let u be a cyclic word in a free group F_n of finite rank n that has the minimum length over all cyclic words in its automorphic orbit, and let N(u) be the cardinality of the set {…
Counting words of minimum length in an automorphic orbit
Donghi Lee
Let u be a cyclic word in a free group F_n of finite rank n that has the minimum length over all cyclic words in its automorphic orbit, and let N(u) be the cardinality of the set {…