Algebraic and Geometric Topology 5 (2005), paper no. 20, pages 443-462.

Signed ordered knotlike quandle presentations

Sam Nelson

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

AMS subject classification. Primary: 57M25, 57M27. Secondary: 27M05, 20F05.

DOI: 10.2140/agt.2005.5.443

E-print: arXiv:math.GT/0408375

Submitted: 14 September 2004. (Revised: 29 March 2005.) Accepted: 8 April 2005. Published: 26 May 2005.

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Sam Nelson
University of California, Riverside
900 University Avenue, Riverside, CA 92521, USA

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