# Intersecting geodesics on a surface from non-intersecting geodesics

Let $a$ and $b$ be non-intersecting closed geodesics on a hyperbolic surface. Can these curves be homotopied to transversely intersect but still be geodesics?

• No. The closed geodesic in a homotopy class is unique. – Lee Mosher Sep 11 '18 at 12:14