The metric space of geodesic laminations on a surface. I. (English) Zbl 1063.57019

Authors’ abstract: We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric \(d_H\) and with a variation of this metric called the \(d_{\log}\) 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.


57M99 General low-dimensional topology
37E35 Flows on surfaces
Full Text: DOI arXiv EuDML EMIS


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