Nielsen equivalence in Fuchsian groups and Heegaard splittings of Seifert spaces
| Full text | |
| Author(s): |
Belolipetsky, Mikhail
;
Cosac, Gregory
;
Doria, Cayo
;
Paula, Gisele Teixeira
Total Authors: 4
|
| Document type: | Journal article |
| Source: | JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES; v. 111, n. 2, p. 17-pg., 2025-02-01. |
| Abstract | |
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) | |
| FAPESP's process: | 22/10772-0 - Arithmeticity in low dimensional geometry |
| Grantee: | Gregory Cosac Daher |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |