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Modular embeddings and rigidity for Fuchsian groups

Volume 169 / 2015

Robert A. Kucharczyk Acta Arithmetica 169 (2015), 77-100 MSC: Primary 20H10, 11F06, 20D60; Secondary 22E40, 14G35. DOI: 10.4064/aa169-1-5

Abstract

We prove a rigidity theorem for semiarithmetic Fuchsian groups: If $\varGamma_1$, $\varGamma_2$ are two semiarithmetic lattices in ${\rm PSL}(2,\mathbb R )$ virtually admitting modular embeddings, and $f\colon\varGamma_1\to\varGamma_2$ is a group isomorphism that respects the notion of congruence subgroups, then $f$ is induced by an inner automorphism of ${\rm PGL}(2,\mathbb R )$.

Authors

  • Robert A. KucharczykMathematisches Institut
    Universität Bonn
    Endenicher Allee 60
    53115 Bonn, Germany
    e-mail

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