Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657687 | Topology | 2007 | 23 Pages |
Abstract
In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More precisely, we first show that for any modular subgroup the geodesic forward dynamic on the associated surface admits a canonical symbolic representation by a finitely irreducible shift space. We then use this representation to derive a complete multifractal description of the higher-dimensional level sets arising from the Manin–Marcolli limiting modular symbols.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
M. Kesseböhmer, B.O. Stratmann,