Journal of Fractal Geometry

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Volume 1, Issue 4, 2014, pp. 427–447
DOI: 10.4171/JFG/13

Published online: 2015-01-06

Rauzy fractals with countable fundamental group

Timo Jolivet[1], Benoît Loridant[2] and Jun Luo[3]

(1) Université Paris Diderot, France
(2) Montanuniversität Leoben, Austria
(3) 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.

Keywords: Rauzy fractal, fundamental group, free group

Jolivet Timo, Loridant Benoît, Luo Jun: Rauzy fractals with countable fundamental group. J. Fractal Geom. 1 (2014), 427-447. doi: 10.4171/JFG/13