What is the homotopy type of the space of (topological) emdeddings of $S^1$ in $\mathbb R^2$? 

My conjecture: This space deformation retracts to $S^1\sqcup S^1$, and a retraction in each of orientation preserving and reversing components is given by  "rotation number". (I don't have an exact proof or even an exact definition of the conjectured retraction map)