Rauzy fractals with countable fundamental group

Autor:	Jolivet, Timo, Loridant, Benoît, Luo, Jun
Rok vydání:	2013
Předmět:	Mathematics - Dynamical Systems Computer Science - Discrete Mathematics Mathematics - Combinatorics
Zdroj:	Journal of Fractal Geometry 1 (2014), no. 4, 427-447
Druh dokumentu:	Working Paper
DOI:	10.4171/JFG/13
Popis:	We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. This 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. Comment: 14 pages, v3 includes some corrections to match the published version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1312.7829 Zobrazit plný text záznamu View this record from Arxiv