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Rauzy fractals with countable fundamental group (1312.7829v3)
Published 30 Dec 2013 in math.DS, cs.DM, and math.CO
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.