The topological biquandle of a link

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.