The geometric biquandle of a knot

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