25 citations · 76 across the 17 of their papers we have counts for
21 papers · 1 filter
A partial resolution of Hedden's conjecture on satellite homomorphisms
Randall Johanningsmeier, Hillary Kim, Allison N. Miller
A pattern knot in a solid torus defines a self-map of the smooth knot concordance group. We prove that if the winding number of a pattern is even but not divisible by 8, then the c…
A note on surfaces in and
Marco Marengon, Allison N. Miller, Arunima Ray +1
In this brief note, we investigate the -genus of knots, i.e. the least genus of a smooth, compact, orientable surface in boun…
Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group
Allison N. Miller, Mark Powell
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let be a genus one strongly invertib…
Linking number obstructions to satellite homomorphisms
Tye Lidman, Allison N. Miller, Juanita Pinzón-Caicedo
We prove that satellite operations that satisfy a certain positivity condition and have winding number other than one are not homomorphisms. The argument uses the -invariants of…
Slicing knots in definite 4-manifolds
Alexandra Kjuchukova, Allison N. Miller, Arunima Ray +1
We study the -slicing number of knots, i.e. the smallest such that a knot bounds a properly embedded, null-homologous disk in a punctured…
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…
Embedding spheres in knot traces
Peter Feller, Allison N. Miller, Matthias Nagel +3
The trace of -framed surgery on a knot in is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a mani…
Branched covers bounding rational homology balls
Paolo Aceto, Jeffrey Meier, Allison N. Miller +3
Prime power fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize slice knots. In this paper, we…
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…
A note on the topological slice genus of satellite knots
Peter Feller, Allison N. Miller, Juanita Pinzon-Caicedo
This paper presents evidence supporting the surprising conjecture that in the topological category the slice genus of a satellite knot is bounded above by the sum of the sli…
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…
Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance
Allison N. Miller, Mark Powell
We give a formula for the duality structure of the 3-manifold obtained by doing zero-framed surgery along a knot in the 3-sphere, starting from a diagram of the knot. We then use t…
Linking forms of amphichiral knots
Stefan Friedl, Allison N. Miller, Mark Powell
We give a simple obstruction for a knot to be amphichiral, in terms of the homology of the 2-fold branched cover. We work with unoriented knots, and so obstruct both positive and n…
Knot traces and concordance
Allison N. Miller, Lisa Piccirillo
We give a method for constructing many pairs of distinct knots and such that the two 4-manifolds obtained by attaching a 2-handle to along with framing zero…
The topological sliceness of 3-strand pretzel knots
Allison N. Miller
We give a complete characterization of the topological slice status of odd 3-strand pretzel knots, proving that an odd 3-strand pretzel knot is topologically slice if and only if e…
Ravels arising from Montesinos Tangles
Erica Flapan, Allison N. Miller
A ravel is a spatial graph which is non-planar but contains no non-trivial knots or links. We characterize when a Montesinos tangle can become a ravel as the result of vertex closu…
A note on the topological sliceness of some 2-bridge knots
Allison N. Miller
We use twisted Alexander polynomials to show that certain algebraically slice 2-bridge knots are not topologically slice, even though all prime power Casson-Gordon signatures vanis…
Distinguishing mutant pretzel knots in concordance
Allison N. Miller
We prove that many pretzel knots of the form are not topologically slice, even though their positive mutants are ribbon. We use the sli…