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arXiv · 1408.3024

Modular Embeddings and Rigidity for Fuchsian Groups

Robert A. Kucharczyk
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Abstract

We prove a rigidity theorem for semi-arithmetic Fuchsian groups: If $\Gamma_1$, $\Gamma_2$ are two semi-arithmetic lattices in $\mathrm{PSL}(2,\mathbb{R})$ virtually admitting modular embeddings and $f\colon\Gamma_1\to\Gamma_2$ is a group isomorphism that respects the notion of congruence subgroups, then $f$ is induced by an inner automorphism of $\mathrm{PGL}(2,\mathbb{R})$.

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BibTeXRIS

Robert A. Kucharczyk. 2014-08-13. Modular Embeddings and Rigidity for Fuchsian Groups. https://arxiv.org/abs/1408.3024

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