Signed ordered knotlike quandle presentations

Nelson, Sam

doi:10.2140/agt.2005.5.443

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Signed ordered knotlike quandle presentations

Sam Nelson

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 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

Volume 5, issue 2 (2005)