13 citations · 38 across the 13 of their papers we have counts for
17 papers
Adjacency of three-manifolds and Brunnian links
Tye Lidman, Allison H. Moore
We introduce the notion of adjacency in three-manifolds. A three-manifold is -adjacent to another three-manifold if there exists an -component link in and surgery…
Determinants of Simple Theta Curves and Symmetric Graphs
Matthew Elpers, Rayan Ibrahim, Allison H. Moore
A theta curve is a spatial embedding of the -graph in the three-sphere, taken up to ambient isotopy. We define the determinant of a theta curve as an integer-valued invariant ar…
Primality of theta-curves with proper rational tangle unknotting number one
Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol +2
We show that if a composite -curve has (proper rational) unknotting number one, then it is the order 2 sum of a (proper rational) unknotting number one knot and a trivial -cu…
Cosmetic operations and Khovanov multicurves
Artem Kotelskiy, Tye Lidman, Allison H. Moore +2
We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invar…
Quotients of the Gordian and H(2)-Gordian graphs
Christopher Flippen, Allison H. Moore, Essak Seddiq
The Gordian graph and H(2)-Gordian graphs of knots are abstract graphs whose vertex sets represent isotopy classes of unoriented knots, and whose edge sets record whether pairs of…
Triple linking numbers and Heegaard Floer homology
Eugene Gorsky, Tye Lidman, Beibei Liu +1
We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex,…