# Gerhard Dorfer: On the fundamental group of the Sierpiński gasket

## This is a joint work with Shigeki Akiyama, Jörg Thuswaldner and Reinhard Winkler.

We give a description of the fundamental group of the Sierpiński gasket as a subgroup of the inverse limit , where is the fundamental group of the -th approximation to that emerges from a triangle by gradually removing open middle triangles. For this purpose we assign to a loop in at each approximation level a word consisting of the (finite) sequence of transition points'' of order which the loop passes in a sense. This way homotopy of loops can be handled by an appropriate reduction process on the corresponding words, and a topological condition characterizes those elements in the inverse limit that effectively represent a loop.