The topological biquandle of a link

Eva Horvat

Vol. 302 (2019), No. 2, 627–644

DOI: 10.2140/pjm.2019.302.627

Abstract

To every oriented link $L$, we associate a topologically defined biquandle ${\widehat{\mathcal{ℬ}}}_L$, which we call the topological biquandle of $L$. The construction of ${\widehat{\mathcal{ℬ}}}_L$ is similar to the topological description of the fundamental quandle given by Matveev. We find a presentation of the topological biquandle and explain how it is related to the fundamental biquandle of the link.

Keywords

biquandle, quandle, fundamental biquandle, topological biquandle

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57M05

Milestones

Received: 9 April 2018

Revised: 18 March 2019

Accepted: 20 March 2019

Published: 27 November 2019