The mapping class group orbit of a multicurve

Details The mapping class group orbit of a multicurve The mapping class group orbit of a multicurve

2008-02-21

arxiv.org/abs/0802.3000v2

Mathematics

Differential Geometry

15 pages, 4 figures, LaTeX; corrected one bibliography entry

Scientific paper

Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus at least two, no such almost invariant coloring exists. Conversely, in the case of a closed torus, one may find almost invariant colorings using arbitrarily many colors.

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