Limiting modular symbols and their fractal geometry
| dc.creator | Kesseböhmer, Marc | |
| dc.creator | Stratmann, Bernd O. | |
| dc.date | 2006-11-02 | |
| dc.date.accessioned | 2026-07-07T08:11:12Z | |
| dc.date.available | 2026-07-07T08:11:12Z | |
| dc.description | 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 an `almost complete' multifractal description of the higher--dimensional level sets arising from Manin--Marcolli's limiting modular symbols. | |
| dc.description | 20 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0611048 | |
| dc.identifier | http://arxiv.org/abs/math/0611048 | |
| dc.identifier | Homology at infinity; fractal geometry of limiting symbols for modular group, Topology 46 (2007), no. 5, 469-49 | |
| dc.identifier | doi:10.1016/j.top.2007.03.004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132049 | |
| dc.subject | Geometric Topology | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Number Theory | |
| dc.subject | 11F06, 20H05, 37F35 | |
| dc.title | Limiting modular symbols and their fractal geometry | |
| dc.type | text |