Combinatorics of Train Tracks. (AM-125), Volume 125

Measured geodesic laminations are a natural generalization of simple closed curves in surfaces. This treatise presents a study of the combinatorial structure of the space of measured geodesic laminations in a fixed surface.

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Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry and dynamical systems. This book presents a self-contained treatment of the combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface.