Topological Quandles and Invariants of Links

We introduce a notion of topological quandle. Given a topological quandle $Q$ we associate to every classical link $L$ in ${\mathbb{R}}^3$ an invariant $J_Q(L)$ which is a topological space (defined up to a homeomorphism). The space $J_Q(L)$ can be interpreted as a space of colourings of a diagram of the link $L$ with colours from the quandle $Q$.