Algebra featuring topology: A few facts on free groups

Wolfgang Moens
(University of Vienna)

Abstract:

In part II of the miniseries on connections between topology and algebra, we will consider free groups; the elements of which are by definition the words in some given alphabet. For example, ABBABABAA and BBBAB are words in the alphabet that consists of the two letters A and B. We will sketch a proof for the famous result: "if a group is free, the so are all of its subgroups." The easiest proof for this algebraic statement comes from topology and we will go through the steps of the proof, illustating it with some examples. As the proof shows us, free groups are closely related to linear graphs, covering spaces, fundamental groups and wedges of circles.