34 citations · 60 across the 15 of their papers we have counts for
20 papers
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…
Non-slice linear combinations of iterated torus knots
Anthony Conway, Min Hoon Kim, Wojciech Politarczyk
In 1976, Rudolph asked whether algebraic knots are linearly independent in the knot concordance group. This paper uses twisted Blanchfield pairings to answer this question in the a…
Homology spheres and property R
Min Hoon Kim, JungHwan Park
We present infinitely many homology spheres which contain two distinct knots whose 0-surgeries are . This resolves a question posed by Kirby and Melvin in 1978.
A family of freely slice good boundary links
Jae Choon Cha, Min Hoon Kim, Mark Powell
We show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all pre…
Pretzel links, mutation, and the slice-ribbon conjecture
Paolo Aceto, Min Hoon Kim, JungHwan Park +1
Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P(p,q,-p,-q) is not slice, even though it has a ribbon mutant, by using 3-fold branched…
Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
Matthew Hedden, Min Hoon Kim, Thomas E. Mark +1
We give two infinite families of examples of closed, orientable, irreducible 3-manifolds such that and has weight 1, but is not the result of Dehn surge…
The bipolar filtration of topologically slice knots
Jae Choon Cha, Min Hoon Kim
The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that…
Ideal classes and Cappell-Shaneson homotopy 4-spheres
Min Hoon Kim, Shohei Yamada
Gompf proposed a conjecture on Cappell-Shaneson matrices whose affirmative answer implies that all Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. W…
The round handle problem
Min Hoon Kim, Mark Powell, Peter Teichner
We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-mani…
Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link
Min Hoon Kim, David Krcatovich, JungHwan Park
We give infinitely many -component links with unknotted components which are topologically concordant to the Hopf link, but not smoothly concordant to any -component link wit…
On rational sliceness of Miyazaki's fibered, amphicheiral knots
Min Hoon Kim, Zhongtao Wu
We prove that certain fibered, amphicheiral knots are rationally slice. Moreover, we show that the concordance invariants and from Heegaard Floer homology vanish fo…
An infinite-rank summand of knots with trivial Alexander polynomial
Min Hoon Kim, Kyungbae Park
We show that there exists a -summand in the subgroup of the knot concordance group generated by knots with trivial Alexander polynomial. To this end we use the i…
Rasmussen s-invariants of satellites do not detect slice knots
Jae Choon Cha, Min Hoon Kim
We present a large family of knots for which the Rasmussen s-invariants of arbitrary satellites do not detect sliceness. This answers a question of Hedden. The proof hinges on work…
Whitney towers, Gropes and Casson-Gordon style invariants of links
Min Hoon Kim
In this paper, we prove a conjecture of Friedl and Powell that their Casson-Gordon type invariant of 2-component link with linking number one is actually an obstruction to being he…
Smoothly slice boundary links whose derivative links have nonvanishing Milnor invariants
Hye Jin Jang, Min Hoon Kim, Mark Powell
We give an example of a 3-component smoothly slice boundary link, each of whose components has a genus one Seifert surface, such that any metaboliser of the boundary link Seifert f…