8 papers
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…
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…