1 citations · 1 across the 6 of their papers we have counts for
7 papers
The -adjacency graph for knots
Marion Campisi, Brandy Doleshal, Eric Staron
A knot is called -adjacent to a knot if there is a set of crossing circles in so that a generalized crossing change at any nonempty subset of cross…
Genus two Goeritz equivalence in lens spaces
Brandy Doleshal, Matt Rathbun
In this paper, we consider the action of the Goeritz group for the genus two Heegaard splitting of the lens space with on the homology of the Heega…
Twisted torus knots with Horadam parameters
Brandy Doleshal
Sangyop Lee has done much work to determine the knot types of twisted torus knots, including classifying the twisted torus knots which are the unknot. Among the unknotted twisted t…
The Jones polynomial for a torus knot with twists
Brandon Bavier, Brandy Doleshal
We compute the Jones polynomial for a three-parameter family of links, the twisted torus links of the form where and are coprime and is nonzero. When $…
Genus 2 Goeritz Equivalence in
Brandy Doleshal, Matt Rathbun
The Goeritz group of a genus Heegaard splitting of a 3-manifold is the group of isotopy classes of orientation-preserving automorphisms of the manifold that preserve the Heegaa…
Additional cases of positive twisted torus knots
Evan Amoranto, Brandy Doleshal, Matt Rathbun
A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in , the genus 2 Heegaard surface for . P…
Fibered and primitive/Seifert twisted torus knots
Brandy Guntel Doleshal
The twisted torus knots lie on the standard genus 2 Heegaard surface for , as do the primitive/primitive and primitive/Seifert knots. It is known that primitive/primitive knot…