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math.GT2021
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…
math.GT2019
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…
math.GT2011
Parity Biquandles
Aaron Kaestner, Louis H. Kauffman
We use crossing parity to construct a generalization of biquandles for virtual knots which we call Parity Biquandles. These structures include all biquandles as a standard example…