Linear structures on measured geodesic laminations
نویسنده
چکیده
The space ML(F ) of measured geodesic laminations on a given compact closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (eartquake theory) or complex projective (grafting) geometry as well in (2 + 1) Lorentzian one (globally hyperbolic spacetimes of constant curvature). We investigate this linear structure, by showing in particular how it heavily depends on the geometric structure of F , while to many other extents ML(F ) only depends on the topology of F . This is already manifest when we describe in geometric terms the sum of two measured geodesic laminations in the simplest non trivial case of two weighted simple closed geodesics that meet each other at one point.
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