10 papers · 1 filter
Smoothly slice knots with smoothly non-approximable topological slice discs
Min Hoon Kim, Mark Powell
We construct infinitely many smoothly slice knots having topological slice discs that are non-approximable by smooth slice discs.
Calegari's homotopy 4-spheres from fibered knots are standard
Jae Choon Cha, Min Hoon Kim
In 2009, Calegari constructed smooth homotopy 4-spheres from monodromies of fibered knots. We prove that all these are diffeomorphic to the standard 4-sphere. Our method uses 5-dim…
A note on rational band moves
Daren Chen, Jennifer Hom, Min Hoon Kim +2
We introduce an oriented rational band move, a generalization of an ordinary oriented band move, and show that if a knot in the three-sphere can be made into the -compon…
Non-slice 3-stranded pretzel knots
Min Hoon Kim, Changhee Lee, Minkyoung Song
Greene-Jabuka and Lecuona confirmed the slice-ribbon conjecture for 3-stranded pretzel knots except for an infinite family where is an odd intege…
Primary decomposition of knot concordance and von Neumann rho-invariants
Min Hoon Kim, Se-Goo Kim, Taehee Kim
We address the primary decomposition of the knot concordance group in terms of the solvable filtration and higher-order von Neumann -invariants by Cochran, Orr, and Teichner. We…
One-bipolar topologically slice knots and primary decomposition
Min Hoon Kim, Se-Goo Kim, Taehee Kim
Let {T_n} be the bipolar filtration of the smooth concordance group of topologically slice knots, which was introduced by Cochran, Harvey, and Horn. It is known that for each n not…