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Winning games for bounded geodesics in moduli spaces of quadratic differentials

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  • We prove that the set of bounded geodesics in Teichmüller space is a winning set for Schmidt's game. This is a notion of largeness in a metric space that can apply to measure $0$ and meager sets. We prove analogous closely related results on any Riemann surface, in any stratum of quadratic differentials, on any Teichmüller disk and for intervals exchanges with any fixed irreducible permutation.
    Mathematics Subject Classification: Primary: 30F30; Secondary: 32G15.


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