16 citations · 25 across the 15 of their papers we have counts for
17 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…
Pseudo knots and an obstruction to cosmetic crossings
Heather A. Dye
Pseudo links have two crossing types: classical crossings and indeterminate crossings. They were first introduced by Ryo Hanaki as a possible tool for analyzing images produced by…
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…
Vassiliev Invariants from Parity Mappings
H. A. Dye
Parity mappings from the chords of a Gauss diagram to the integers is defined. The parity of the chords is used to construct families of invariants of Gauss diagrams and virtual kn…
Smoothed Invariants
H. A. Dye
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots ob…
Invariants from the Linking Number
H. A. Dye
We explore a family of invariants obtained from linking numbers. This is a family of Kauffman finite type invariants.