 
Summary: ON THE FUNDAMENTAL GROUP OF THE
SIERPI ŽNSKIGASKET
S. AKIYAMA, G. DORFER, J. M. THUSWALDNER, AND R. WINKLER
Dedicated to Professor Peter Kirschenhofer on the occasion of his 50th birthday
Abstract. We give a description of the fundamental group ( ) of the
SierpiŽnskigasket . It turns out that this group is isomorphic to a certain
subgroup of an inverse limit lim

Gn formed by the fundamental groups Gn
of natural approximations of . This subgroup, and with it ( ), can be
described in terms of sequences of words contained in an inverse limit of semi
groups.
1. Introduction
The present paper is devoted to the description of the fundamental group of
the SierpiŽnskigasket (see Figure 1). It turns out that this fundamental group
can be viewed as a subset of an inverse limit of the fundamental groups of certain
natural approximations of . Before we give more details we would like to state
some definitions and earlier results that are related to our topic.
Figure 1. The SierpiŽnskigasket
Date: December 16, 2008.
