Graphs and triangles of groups

Abstract

Bass-Serre theory studies group actions on trees, unifying two combinatorial constructions from group theory, namely free product with amalgamation and the HNN extension, which are understood as special cases of graphs of groups. This talk will give an introduction to Bass-Serre theory up to and including its so-called fundamental theorem. We will also introduce Gersten and Stallings' notion of non-positively curved triangles of groups, as a first step towards the more general theory of complexes of groups.