The metric space of geodesic laminations on a surface II: small surfaces
نویسندگان
چکیده
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. AMS Classification numbers Primary: 57M99, 37E35
منابع مشابه
The metric space of geodesic laminations on a surface: I
We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric dH and with a variation of this metric called the dlog metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these two metrics to another metric which is combinatorially defined in terms of train tracks. AMS Classification numbers Primary: 57M99
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