Volume 5, issue 2 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Signed ordered knotlike quandle presentations

Sam Nelson

Algebraic & Geometric Topology 5 (2005) 443–462

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 2000
Primary: 57M25, 57M27
Secondary: 20F05
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Publication
Received: 14 September 2004
Revised: 29 March 2005
Accepted: 8 April 2005
Published: 26 May 2005
Authors
Sam Nelson
University of California, Riverside
900 University Avenue
Riverside CA 92521
USA