Semiquandles and flat virtual knots

Allison Henrich and Sam Nelson

Vol. 248 (2010), No. 1, 155–170

DOI: 10.2140/pjm.2010.248.155

Abstract

We define an algebraic structure we call a semiquandle, whose axioms are derived from the 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.

Keywords

flat knots and links, virtual knots and links, singular knots and links, semiquandles, Vassiliev invariants

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

Milestones

Received: 28 April 2009

Accepted: 29 June 2010

Published: 1 October 2010