2 citations · 2 across the 4 of their papers we have counts for
9 papers
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…
Amphichiral knots with large 4-genus
Allison N. Miller
For each we give infinitely many knots that are strongly negative amphichiral, hence rationally slice and representing 2-torsion in the smooth concordance group, yet which do…
Homomorphism obstructions for satellite maps
Allison N. Miller
A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in . This set admits a group structure, but a conjecture of Hedden sug…
Stabilization distance between surfaces
Allison N. Miller, Mark Powell
Define the 1-handle stabilization distance between two surfaces properly embedded in a fixed 4-dimensional manifold to be the minimal number of 1-handle stabilizations necessary fo…
Two-solvable and two-bipolar knots with large four-genera
Jae Choon Cha, Allison N. Miller, Mark Powell
For every integer g, we construct a 2-solvable and 2-bipolar knot whose topological 4-genus is greater than g. Note that 2-solvable knots are in particular algebraically slice and…
Winding number and patterns acting on concordance
Allison N. Miller
We prove that for any winding number pattern and winding number pattern , there exist knots such that the minimal genus of a cobordism between and $Q(K…