8 citations · 20 across the 16 of their papers we have counts for
17 papers
Satellites and telescopes: a concordance formula for bordered Floer homology
Gary Guth, Sungkyung Kang
Given a knot in , its knot Floer completely determines the bordered Floer homology of its complement by a work of Lipshitz--Ozsváth--Thurston. Furthermore, the determinati…
Topologically and rationally slice knots
Jennifer Hom, Sungkyung Kang, JungHwan Park
A knot in is topologically slice if it bounds a locally flat disk in . A knot in is rationally slice if it bounds a smooth disk in a rational homology ball. We pro…
One stabilization is not enough for closed knotted surfaces
Kyle Hayden, Sungkyung Kang, Anubhav Mukherjee
In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either exter…
One stabilization is not enough for contractible 4-manifolds
Sungkyung Kang
We construct an example of a cork that remains exotic after taking a connected sum with . Combined with a work of Akbulut-Ruberman, this implies the existence of an…
Torsion in the knot concordance group and cabling
Sungkyung Kang, JungHwan Park
We define a nontrivial mod 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not…
The -cable of the figure-eight knot is not smoothly slice
Irving Dai, Sungkyung Kang, Abhishek Mallick +2
We prove that the -cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.
Involutive knot Floer homology and bordered modules
Sungkyung Kang
We prove that, up to local equivalences, a suitable truncation of the involutive knot Floer homology of a knot in and the involutive bordered Heegaard Floer theory of its com…
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…
On the nonorientable four-ball genus of torus knots
Fraser Binns, Sungkyung Kang, Jonathan Simone +1
The nonorientable four-ball genus of a knot in is the minimal first Betti number of nonorientable surfaces in bounded by . By amalgamating ideas from involutive…
Linear independence of rationally slice knots
Jennifer Hom, Sungkyung Kang, JungHwan Park +1
A knot in is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot…
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…
Ribbon knots, cabling, and handle decompositions
Jennifer Hom, Sungkyung Kang, JungHwan Park
The fusion number of a ribbon knot is the minimal number of 1-handles needed to construct a ribbon disk. The strong homotopy fusion number of a ribbon knot is the minimal number of…
Link homology theories and ribbon concordances
Sungkyung Kang
It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched…
Connected Floer homology of covering involutions
Antonio Alfieri, Sungkyung Kang, Andras I. Stipsicz
Using the covering involution on the double branched cover of the three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu and Hendricks-Hom-Lidman, we define…
-equivariant Heegaard Floer cohomology of knots in as a strong Heegaard invariant
Sungkyung Kang
The -equivariant Heegaard Floer cohomlogy of a knot in , constructed by Hendricks, Lipshitz, and Sarkar, is an isot…
A transverse knot invariant from Z2-equivariant Heegaard Floer cohomology
Sungkyung Kang
We define an invariant of based transverse links, as a well-defined element inside the equivariant Heegaard Floer cohomology of its branched double cover, defined by Lipschitz, Hen…
Spectral order for contact manifolds with convex boundary
András Juhász, Sungkyung Kang
We extend the Heegaard Floer homological definition of spectral order for closed contact 3-manifolds due to Kutluhan, Matić, Van Horn-Morris, and Wand to contact 3-manifolds with c…