Homology at infinity; fractal geometry of limiting symbols for modular subgroups

Bernd O Stratmann, M Kesseboehmer

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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. (C) 2007 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)469-491
Number of pages23
Issue number5
Publication statusPublished - Sept 2007


  • limiting modular symbols
  • modular subgroups
  • non-commutative tori
  • thermodynamical formalism
  • multifractal formalism
  • Lyapunov spectra


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