Given a compact, oriented surface $S$ of finite genus and finitely many boundary components, we provide examples of finite covers $\tilde{ S}$ of $S$ and non-simple closed curves $\gamma$ on $S$ which lifts to simple closed curves on $\tilde{ S}$. In particular, given any positive integer $n\geq 2$, we construct explicit non-simple closed curves on $S$ which has a simple lift to a degree $n$ cover of $S$.
Categories: math.GT