Geometry and arithmetic of semi-arithmetic Fuchsian groups

Autor(es)

Belolipetsky, Mikhail ; Cosac, Gregory ; Doria, Cayo ; Paula, Gisele Teixeira

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES; v. 111, n. 2, p. 17-pg., 2025-02-01.

Resumo

Semi-arithmetic Fuchsian groups is a wide class of discrete groups of isometries of the hyperbolic plane which includes arithmetic Fuchsian groups, hyperbolic triangle groups, groups admitting a modular embedding, and others. We introduce a new geometric invariant of a semi-arithmetic group called stretch. Its definition is based on the notion of the Riemannian center of mass developed by Karcher and collaborators. We show that there exist only finitely many conjugacy classes of semi-arithmetic groups with bounded arithmetic dimension, stretch and coarea. The proof of this result uses the arithmetic Margulis lemma. We also show that when stretch is not bounded there exist infinite sequences of such groups. (AU)

• Processo FAPESP: 22/10772-0 - Aritmeticidade em geometria de baixa dimensão
• Beneficiário: Gregory Cosac Daher
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado