Modular embeddings and rigidity for Fuchsian groups

Robert A. Kucharczyk¹

¹ Mathematisches Institut Universität Bonn Endenicher Allee 60 53115 Bonn, Germany

Acta Arithmetica, Tome 169 (2015) no. 1, pp. 77-100.

Résumé

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 ${\rm PGL}(2,\mathbb R )$.

Détail

DOI : 10.4064/aa169-1-5

Keywords: prove rigidity theorem semiarithmetic fuchsian groups vargamma vargamma semiarithmetic lattices psl mathbb virtually admitting modular embeddings colon vargamma vargamma group isomorphism respects notion congruence subgroups induced inner automorphism nbsp pgl mathbb