16 citations · 41 across the 13 of their papers we have counts for
15 papers
Non-isotopic splitting spheres for a split link in
Mark Hughes, Seungwon Kim, Maggie Miller
We show that there exist split, orientable, 2-component surface-links in with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m…
Unknotting via null-homologous twists and multi-twists
Samantha Allen, Kenan Ince, Seungwon Kim +2
The untwisting number of a knot K is the minimum number of null-homologous twists required to convert K to the unknot. Such a twist can be viewed as a generalization of a crossing…
Seifert surfaces in the 4-ball
Kyle Hayden, Seungwon Kim, Maggie Miller +2
We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in that do not become isotopic when their interiors are pushed into $B…
Knotted handlebodies in the 4-sphere and 5-ball
Mark Hughes, Seungwon Kim, Maggie Miller
For every integer we construct 3-dimensional genus- 1-handlebodies smoothly embedded in with the same boundary, and which are defined by the same cut systems of t…
Stabilization and satellite construction of doubly slice links
Hongtaek Jung, Sungkyung Kang, Seungwon Kim
A 2-component oriented link in is called weakly doubly slice if it is a cross-section of an unknotted sphere in , and strongly doubly slice if it is a cross-section of a…
Band diagrams of immersed surfaces in 4-manifolds
Mark Hughes, Seungwon Kim, Maggie Miller
We study immersed surfaces in smooth 4-manifolds via singular banded unlink diagrams. Such a diagram consists of a singular link with bands inside a Kirby diagram of the ambient 4-…
Gluck twist and unknotting of satellite -knots
Seungwon Kim
In this paper, we show that the Gluck twist of certain satellite -knots in a -manifold do not change the diffeomorphism type in three different ways: one is directly from the…
Concordance invariants and the Turaev genus
Hongtaek Jung, Sungkyung Kang, Seungwon Kim
We show that the differences between various concordance invariants of knots, including Rasmussen's -invariant and its generalizations -invariants, give lower bounds to the…
Turaev Surfaces
Seungwon Kim, Ilya Kofman
An expository article on Turaev surfaces written for "A Concise Encyclopedia of Knot Theory," to appear.
Trisections of surface complements and the Price twist
Seungwon Kim, Maggie Miller
Given an smoothly embedded in a 4-manifold with Euler number 2 or -2, the Price twist is a surgery operation on yielding (up to) three different…
Isotopies of surfaces in 4-manifolds via banded unlink diagrams
Mark C. Hughes, Seungwon Kim, Maggie Miller
In this paper, we study surfaces embedded in -manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary -manifold. This…
Immersed Möbius bands in knot complements and representatives of -homology classes
Mark C. Hughes, Seungwon Kim
We study the 3-dimensional immersed crosscap number of a knot, which is a nonorientable analogue of the immersed Seifert genus. We study knots with immersed crosscap number 1, and…
Representativity and waist of cable knots
Román Aranda, Seungwon Kim, Maggy Tomova
We study the incompressible surfaces in the exterior of a cable knot and use this to compute the representativity and waist of most cable knots.
A topological characterization of toroidally alternating knots
Seungwon Kim
We extend Howie's characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary an…
Link diagrams with low Turaev genus
Seungwon Kim
We classify link diagrams with Turaev genus one and two in terms of an alternating tangle structure of the link diagram. The proof involves surgery along simple closed curves on th…