Let Sigma be a compact orientable surface. Suppose that its fundamental group acts on a Gromov hyperbolic space with hausdorff quotient M. Given any multicurve in Sigma, we can define a shortest realisation in M. Under certain assumptions of the action, we show that such a realisation is supported, up to bounded distance, by a train track realised in M. One purpose of this is to show that certain results in the geometry of hyperbolic 3-manifolds generalise to this context.
September 2010.