University of Arkansas Topology Seminar: 2/25/2016

Speaker: Matt Day

Title: Link splitting complexes and right-angled Artin groups

This is joint work with Henry Wilton. A right-angled Artin group has certain decompositions as an HNN extension based on its defining graph. A "link splitting" of a group is a decomposition that resembles one of these algebraically. We build a simplicial complex, the "link splitting complex" of a group, whose vertices are link splittings, and whose edges correspond to actions on cube complexes that degenerate to link splittings. I will exhibit the behavior of link splitting complexes in several examples.