1 citations · 1 across the 3 of their papers we have counts for
7 papers
Virtual Knot Groups
Heather A. Dye, Aaron Kaestner
For a knot diagram , the classical knot group is a free group modulo relations determined by Wirtinger-type relations on the classical crossings. The classical knot gro…
Virtual Parity Alexander Polynomial
Heather A. Dye, Aaron Kaestner
In this paper, we define the parity virtual Alexander polynomial following the work of BDGGHN [1] and Kaestner and Kauffman [10]. The properties of this invariant are explored and…
Virtual Covers of Links II
Micah Chrisman, Aaron Kaestner
A fibered concordance of knots, introduced by Harer, is a concordance between fibered knots that is well-behaved with respect to the fibrations. We consider semi-fibered concordanc…
Parity Biquandle Invariants of Virtual Knots
Aaron Kaestner, Sam Nelson, Leo Selker
We define counting and cocycle enhancement invariants of virtual knots using parity biquandles. These invariants are determined by pairs consisting of a biquandle 2-cocycle ϕ^0 and…
Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots
Heather A. Dye, Aaron Kaestner, Louis H. Kauffman
The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordi…
Parity, Skein Polynomials and Categorification
Aaron Kaestner, Louis H. Kauffman
We investigate an application of crossing parity for the bracket expansion of the Jones polynomial for virtual knots. In addition we consider an application of parity for the arrow…