Rauzy fractals with countable fundamental group
نویسندگان
چکیده
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.
منابع مشابه
Rauzy fractals with countable fundamental groups
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.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1312.7829 شماره
صفحات -
تاریخ انتشار 2013