The mapping class group orbit of a multicurve

Abstract

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.

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

References in corpus (1)

• Degree one cohomology with twisted coefficients of the mapping class group

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