Geodesic laminations and continued fractions

Details Geodesic laminations and continued fractions Geodesic laminations and continued fractions

2004-03-17

arxiv.org/abs/math/0403295v4

Mathematics

Geometric Topology

11 pages, 1 figure; revised

Scientific paper

The topological invariant of a family of geodesic laminations on the modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant is complete, i.e. the geodesic lamination can be recovered from the invariant. The continuous part of the invariant has geometric meaning of the slope of lamination on the modular surface.

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