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BIQUANDLES OF SMALL SIZE AND SOME INVARIANTS OF VIRTUAL AND WELDED KNOTS

Corrections for this article
- Erratum: Biquandles of small size and some invariants of virtual and welded knots

ANDREW BARTHOLOMEW

School of Mathematical Sciences, University of Sussex, Falmer, Brighton, BN1 9RH, UK

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and

School of Mathematical Sciences, University of Sussex, Falmer, Brighton, BN1 9RH, UK

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https://doi.org/10.1142/S0218216511009042Cited by:7 (Source: Crossref)

Abstract

In this paper we give the results of a computer search for biracks of small size and we give various interpretations of these findings. The list includes biquandles, racks and quandles together with new invariants of welded knots and examples of welded knots which are shown to be non-trivial by the new invariants. These can be used to answer various questions concerning virtual and welded knots. As an application we reprove the result that the Burau map from braids to matrices is non-injective and give an example of a non-trivial virtual (welded) knot which cannot be distinguished from the unknot by any linear biquandles.

Dedicated to Jose Maria Montesinos on the occasion of his 65th birthday

Keywords:

AMSC: 57M25

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Vol. 20, No. 07

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History

Accepted 15 April 2010

Keywords