We prove a rigidity theorem for semiarithmetic Fuchsian groups: If Γ₁, Γ₂ are two semiarithmetic lattices in PSL(2,ℝ ) virtually admitting modular embeddings, and f: Γ₁ → Γ₂ is a group isomorphism that respects the notion of congruence subgroups, then f is induced by an inner automorphism of PGL(2,ℝ ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-1-5,
author = {Robert A. Kucharczyk},
title = {Modular embeddings and rigidity for Fuchsian groups},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {77-100},
zbl = {1325.20044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-1-5}
}
Robert A. Kucharczyk. Modular embeddings and rigidity for Fuchsian groups. Acta Arithmetica, Tome 168 (2015) pp. 77-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-1-5/