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arXiv · 0802.3000

The mapping class group orbit of a multicurve

Rasmus Villemoes
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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.

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Rasmus Villemoes. 2009-03-16. The mapping class group orbit of a multicurve. https://arxiv.org/abs/0802.3000

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