Volumes of Hyperbolic Three-Manifolds Associated with Modular Links

Autor:	Alex Brandts, Tali Pinsky, Lior Silberman
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	modular group primitive geodesics hyperbolic volume Mathematics QA1-939
Zdroj:	Symmetry, Vol 11, Iss 10, p 1206 (2019)
Druh dokumentu:	article
ISSN:	2073-8994
DOI:	10.3390/sym11101206
Popis:	Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle PSL 2 ( Z ) ∖ PSL 2 ( R ) . A finite collection of such orbits is a collection of disjoint closed curves in a 3-manifold, in other words a link. The complement of those links is always a hyperbolic 3-manifold, and hence has a well-defined volume. We present strong numerical evidence that, in the case of the set of geodesics corresponding to the ideal class group of a real quadratic field, the volume has linear asymptotics in terms of the total length of the geodesics. This is not the case for general sets of geodesics.
Databáze:	Directory of Open Access Journals
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