Parity, Skein Polynomials and Categorification
Aaron Kaestner, Louis H. Kauffman
TL;DR
This paper explores the use of crossing parity in the computation and categorification of virtual knot invariants like the Jones polynomial and arrow polynomial, supported by computational examples.
Contribution
It introduces novel applications of crossing parity to virtual knot polynomials and their categorifications, with extensive computational data.
Findings
Parity enhances the computation of virtual knot invariants.
New examples of virtual knots with computed invariants are provided.
Tables of invariants for knots with up to 4 crossings are included.
Abstract
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 polynomial as well as for the categorifications of both polynomials. We present a number of examples found through our calculations. We provide tables of calculations for these invariants on virtual knots with at most 4 real crossings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.