Word sequences have been originally created as a self-contained combinatorial concept for describing that subgroup of the inverse limit of free groups that naturally corresponds to the fundamental group of the Hawaiian Earrings. They are based on an approximization philosophy, that makes the results comparable with the results of shape theory. Word sequences have been proposed as a natural research tool for studying properties of this group and of the natural action of this group on the generalized covering space that can be constructed for the Hawaiian Earrings. Later the concept of word sequences has been generalized to describe all paths in partially filled Modified Sierpinski Carpets. This is a class of spaces that is general enough for containing homotopy equivalent models of all planar Peano continua.
The talk will explain both concepts of word sequences and review the results that could be achieved by this method. Amongst them is the asphericity and acyclicity of all planar sets, and the relation between the fundamental group and the shape group of subsets of surfaces. The latter was a joint research project with Hanspeter Fischer.
