We continue our investigation of the space of geodesic laminations on a
surface, endowed with the Hausdorff topology. We determine the topology of this
space for the once-punctured torus and the 4-times-punctured sphere. For these
two surfaces, we also compute the Hausdorff dimension of the space of geodesic
laminations, when it is endowed with the natural metric which, for small
distances, is -1 over the logarithm of the Hausdorff metric. The key ingredient
is an estimate of the Hausdorff metric between two simple closed geodesics in
terms of their respective slopes.Comment: Published by Geometry and Topology Monographs at
http://www.maths.warwick.ac.uk/gt/GTMon7/paper17.abs.htm
