University of Arkansas Topology Seminar: 2/13/2014

Speaker: Matt Day

Title: Splittings of right-angled Artin groups over links, and applications

Abstract: I will discuss work in progress, joint with Henry Wilton, on right-angled Artin groups (raags). We formulate a definition of the "algebraic link" of an element of a raag; this generalizes the relationship between a standard generator of a raag and the subgroup generated by its link in the defining graph. We study HNN splittings of raags where the edge group is the algebraic link of the stable letter (this is a certain kind of action on a tree). Our main result is that every such splitting is the image of an "obvious" one under an automorphism. We also develop a new inductive scheme for studying automorphism groups of raags, and apply the main result to reprove some classic results about raags, including Laurence's theorem (which gives generators for the automorphism group of a raag).