Algebraic & Geometric Topology 5 (2005) 443–462

DOI: 10.2140/agt.2005.5.443

arXiv: math.GT/0408375

Abstract

We define enhanced presentations of quandles via generators and relations with additional information comprising signed operations and an order structure on the set of generators. Such a presentation determines a virtual link diagram up to virtual moves. We list formal Reidemeister moves in which Tietze moves on the presented quandle are accompanied by corresponding changes to the order structure. Omitting the order structure corresponds to replacing virtual isotopy by welded isotopy.

Keywords

quandles, virtual knots, presentations, Reidemeister moves, welded isotopy

Mathematical Subject Classification

Primary: 57M25, 57M27

Secondary: 20F05

References

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Publication

Received: 14 September 2004
Revised: 29 March 2005
Accepted: 8 April 2005
Published: 26 May 2005

Authors