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Confusion about Teichmüller curves and $\operatorname{SL}_2$-action
$\DeclareMathOperator\SL{SL}$Let $M_g$ be the moduli space of curves, $\Omega M_g$ the total space of the bundle of holomorphic 1-forms and $\pi: \Omega M_g\to M_g$ the natural projection. On $\Omega ...
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Ratner theorem and dense geodesic planes in hyperbolic manifolds
Suppose we have a closed hyperbolic $3$-manifold $M$. For any $x\in M$ and plane $\pi$ in $T_xM$ we consider $P$ the geodesic plane exp$(\pi)$ originating from $\pi$. For any $p\in \pi$ we consider ...