Rauzy fractals with countable fundamental group
Rauzy fractals with countable fundamental group
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DOI：
10.4171/jfg/13
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发表时间：
2013-12
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通讯作者：
Timo Jolivet;B. Loridant;J. Luo
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文献类型：
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作者：
Timo Jolivet;B. Loridant;J. Luo
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.
