The topological biquandle of a link

To every oriented link $L$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>$ , we associate a topologically defined biquandle ${ˆ B}_{L}$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mover accent="false"><mrow><mi mathvariant="bold-script">ℬ</mi></mrow><mo class="MathClass-op">̂</mo></mover></mrow><mrow><mi>L</mi></mrow></msub></math>$ , which we call the topological biquandle of $L$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>$ . The construction of ${ˆ B}_{L}$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mover accent="false"><mrow><mi mathvariant="bold-script">ℬ</mi></mrow><mo class="MathClass-op">̂</mo></mover></mrow><mrow><mi>L</mi></mrow></msub></math>$ 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

Authors

Eva Horvat
Faculty of Education University of Ljubljana Slovenia

Vol. 302, No. 2, 2019

Eva Horvat

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors