## 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.

### MSC:

 57M99 General low-dimensional topology 37E35 Flows on surfaces

### Keywords:

geodesic lamination; simple closed curve
Full Text:

### References:

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