Rauzy fractals with countable fundamental group
Dynamical Systems
2016-03-11 v3 Discrete Mathematics
Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1312.7829,
title = {Rauzy fractals with countable fundamental group},
author = {Timo Jolivet and Benoît Loridant and Jun Luo},
journal= {arXiv preprint arXiv:1312.7829},
year = {2016}
}
Comments
14 pages, v3 includes some corrections to match the published version