Rauzy fractals with countable fundamental group

  • Timo Jolivet

    Université Paris Diderot, France
  • Benoît Loridant

    Montanuniversität Leoben, Austria
  • Jun Luo

    Sun Yat-Sen University, Guangzhou, Guangdong, China


We prove that every free group of nite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. is characterizes all countable fundamental groups for planar Rauzy fractals. We give an explicit construction relying on two operations on substitutions: symbolic splittings and conjugations by free group automorphisms.

Cite this article

Timo Jolivet, Benoît Loridant, Jun Luo, Rauzy fractals with countable fundamental group. J. Fractal Geom. 1 (2014), no. 4, pp. 427–447

DOI 10.4171/JFG/13