Semiquandles and flat virtual knots
Allison Henrich, Sam Nelson
TL;DR
This paper introduces semiquandles, an algebraic structure derived from flat Reidemeister moves, along with their variants, to define invariants for flat virtual knots and links, enhancing knot classification methods.
Contribution
It presents the novel concept of semiquandles and their variants, providing new algebraic tools for analyzing flat virtual knots and links.
Findings
Finite semiquandles yield counting invariants.
Enhanced invariants are defined for flat virtual knots.
Semiquandle invariants compare different Vassiliev invariants.
Abstract
We introduce an algebraic structure we call semiquandles whose axioms are derived from flat Reidemeister moves. Finite semiquandles have associated counting invariants and enhanced invariants defined for flat virtual knots and links. We also introduce singular semiquandles and virtual singular semiquandles which define invariants of flat singular virtual knots and links. As an application, we use semiquandle invariants to compare two Vassiliev invariants.
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