13 papers · 1 filter
A note on the concordance -genus
Allison N. Miller, JungHwan Park
We show that the difference between the topological 4-genus of a knot and the minimal genus of a surface bounded by that knot that can be decomposed into a smooth concordance follo…
The -genus of boundary links
Peter Feller, JungHwan Park, Mark Powell
The -genus of a link in is the minimal genus of a locally flat, embedded, connected surface in whose boundary is and with the fundamental group of t…
Non-simply connected symplectic fillings of lens spaces
Paolo Aceto, Duncan McCoy, JungHwan Park
We prove results exploring the relationship between the fundamental group and the second Betti number of minimal symplectic fillings of lens spaces. These results unify and general…
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…
Genus one cobordisms between torus knots
Peter Feller, JungHwan Park
We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using from the Heegaard…
Concordance to links with an unknotted component
Christopher William Davis, JungHwan Park
We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use co…