### On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number.

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We prove, for any $n$, that there is a closed connected orientable surface $S$ so that the hyperbolic space ${\mathbb{H}}^{n}$ almost-isometrically embeds into the Teichmüller space of $S$, with quasi-convex image lying in the thick part. As a consequence, ${\mathbb{H}}^{n}$ quasi-isometrically embeds in the curve complex of $S$.

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