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Session 37. Wild algebraic and geometric topology
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Fundamental group of Rauzy fractals |
Benoît Loridant, Montanuniversität Leoben, Austria
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The talk is based on the joint work with Timo Jolivet and Jun Luo
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We are interested in the fundamental group of special classes of graph directed self-affine sets associated with substitution dynamical systems, called
Rauzy fractals. There are many known examples of Rauzy fractals which are homeomorphic to the closed disk or whose fundamental group is uncountable. We show that the intermediate situation, with countable fundamental group, occurs. More precisely, we obtain that every group of finite rank can be realized as the fundamental group of a planar Rauzy fractal and give an explicit construction.
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