Vol. 248, No. 1, 2010

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Semiquandles and flat virtual knots

Allison Henrich and Sam Nelson

Vol. 248 (2010), No. 1, 155–170

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.

flat knots and links, virtual knots and links, singular knots and links, semiquandles, Vassiliev invariants
Mathematical Subject Classification 2000
Primary: 57M25, 57M27
Received: 28 April 2009
Accepted: 29 June 2010
Published: 1 October 2010
Allison Henrich
Seattle University
Mathematics Department
901 12th Avenue
PO Box 22200
Seattle, WA 98122
United States
Sam Nelson
Claremont McKenna College
Department of Mathematical Sciences
850 Columbia Ave
Claremont CA, 91711
United States