Abstract
Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle PSL2(Z)nPSL2(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.
Original language | English |
---|---|
Article number | 1206 |
Journal | Symmetry |
Volume | 11 |
Issue number | 10 |
DOIs | |
State | Published - 1 Oct 2019 |
Keywords
- Hyperbolic volume
- Modular group
- Primitive geodesics
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)