A digital description of the fundamental group of fractals I

Gerhard Dorfer

Technische Universität Wien, Austria

Coauthor(s): Shigeki Akiyama, Jörg Thuswaldner, and Reinhard Winkler

In joint work with Shigeki Akiyama, Jörg Thuswaldner and Reinhard Winkler we gave a description of the fundamental group of the Sierpinski-gasket $\bigtriangleup$. The method we used there employs a combinatorial word structure to represent loops in a sequence of approximating spaces $\bigtriangleup_n$. In this way the fundamental group of $\bigtriangleup$ can be characterized as a subgroup of the inverse limit of the fundamental groups of $\bigtriangleup_n$. This approach turns out to be applicable quite generally.

In this talk the method will be presented with focus on the Sierpinski-gasket and the Hawaiian earring. In a subsequent talk Reinhard Winkler will extend this technique to a wide class of spaces.

This work was supported by the Austrian Science Foundation FWF, projects S9612 and S9610.