Rauzy fractals with countable fundamental group
نویسندگان
چکیده
منابع مشابه
Rauzy fractals with countable fundamental group
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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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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1 Departamento de Matemática, IBILCE, UNESP-Universidade Estadual Paulista, 15054-000–São José do Rio Preto, Brazil. E-mail: [email protected] 2 Departamento de Matemática, IBILCE, UNESP-Universidade Estadual Paulista, 15054-000–São José do Rio Preto, Brazil. E-mail: [email protected] 3 Departamento de Matemática, FC, UNESP-Universidade Estadual Paulista, 17033-360–Bauru, Brazil. ...
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ژورنال
عنوان ژورنال: Journal of Fractal Geometry
سال: 2014
ISSN: 2308-1309
DOI: 10.4171/jfg/13