%0 Journal Article
%T The mapping class group orbit of a multicurve
%A Rasmus Villemoes
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0802.3000v2