A digital description of the fundamental group of fractals II

Reinhard Winkler

Technische Universität Wien, Austria

Coauthor(s): Gerhard Dorfer, Benoît Loridant, Christian Steineder, and Jörg Thuswaldner

This talk is connected with Gerhard Dorfer's talk where a description of the fundamental group of special fractals like the Sierpinski gasket (triangle) $\bigtriangleup$ has been presented. In cooperation with him, Benoit Loridant, Christian Steineder and Jörg Thuswaldner we could extend this description to a larger class of plane spaces, namely to all locally path connected one-dimensional continua (i.e. compact and connected sets) in the plane. This class includes for instance the Sierpinski carpet $\Box$ which arises by dividing a square in nine equal parts, removing the open central one, proceeding with the remaining ones in the same way and iterating this procedure until infinity. In contrast to $\bigtriangleup$, there are no finite cut sets of $\Box$. This causes certain complications and requires a generalization of the method in such a way that zero dimensional cut sets play the corresponding role. The goal of my talk is to explain which additional arguments are necessary for this generalization.

This work was supported by the Austrian Science Foundation FWF, project S9612.