Modular embeddings and rigidity for Fuchsian groups
Volume 169 / 2015
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 ${\rm PGL}(2,\mathbb R )$.
