Workshop on Dynamical Systems and Aperiodic Order
Bielefeld University, Germany
14th - 17th March 2011
All talks take place in Room V3-201 ("Common Room") in the Bielefeld
University main building.
Click here for
a description of the main building.
Topological properties of self-affine tiles
Jörg Thuswaldner
Abstract:
In this talk we want to survey results on topological properties
of self-affine sets. We start with results of Hata on connectivity
as well as criteria on arclikeness. In a second part we discuss
topological properties of self-affine subsets of the plane. Here
the Jordan curve theorem and its consequences allows to give
quite simple criteria for the homeomorphy to a disk. In the last
part we deal with representations of self-affine fractals as metric
projective limits. Together with methods from low dimensional
topology such representations enable us to prove topological
results on self-affine sets also in higher dimensions.
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