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ON THE FUNDAMENTAL GROUP OF THE SIERPI NSKI-GASKET
 

Summary: ON THE FUNDAMENTAL GROUP OF THE
SIERPI ŽNSKI-GASKET
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
SierpiŽnski-gasket . 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 SierpiŽnski-gasket (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 SierpiŽnski-gasket
Date: December 16, 2008.

  

Source: Akiyama, Shigeki - Department of Mathematics, Niigata University

 

Collections: Mathematics