Biquasiles and Dual Graph Diagrams

Authors

Deanna Needell, Claremont McKenna CollegeFollow
Sam Nelson, Claremont McKenna CollegeFollow

Document Type

Article - preprint

Department

Claremont McKenna College, Mathematics (CMC)

Publication Date

10-2016

Abstract

We introduce dual graph diagrams representing oriented knots and links. We use these combinatorial structures to define corresponding algebraic structures we call biquasiles whose axioms are motivated by dual graph Reidemeister moves, generalizing the Dehn presentation of the knot group analogously to the way quandles and biquandles generalize the Wirtinger presentation. We use these structures to define invariants of oriented knots and links. In particular, we identify an example of a finite biquasile whose counting invariant distinguishes the chiral knot 9-32 from its mirror image, demonstrating that biquasile counting invariants are distinct from biquandle counting invariants.

Rights Information

© 2016 Needell, Nelson

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

D. Needell and S. Nelson. “Biquasiles and Dual Graph Diagrams.” 2016.