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Coarse density of projection of strata to moduli space Dozier, Benjamin


There is a natural forgetful map p from a stratum H of abelian differentials to the moduli space of Riemann surfaces that takes a pair (X,w) to X. What are the coarse properties of this map p In particular, when is the image coarsely dense with respect to the Teichmuller metric on moduli space We answer this question for all strata by showing that the projection is coarsely dense iff it is topologically dense. The proof uses a new compactification of strata due to Bainbridge-Chen-Gendron-Grushevsky-Moller. This is joint work with Jenya Sapir.

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