Rauzy fractals with countable fundamental group
Timo Jolivet
Université Paris Diderot, FranceBenoît Loridant
Montanuniversität Leoben, AustriaJun Luo
Sun Yat-Sen University, Guangzhou, Guangdong, China
![Rauzy fractals with countable fundamental group cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jfg-volume-1-issue-4.png&w=3840&q=90)
Abstract
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