Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Arrangements, groups, and graphs

An arrangement group is the fundamental group of the complement of a union of hyperplanes in a complex linear or projective space. Based on a notion of "Brunnian elements" in finitely-generated groups, we describe representations of arrangement groups into products of free groups, and give conditions under which such representations are faithful. We draw consequences concerning residual properties and homological finiteness type for certain families of arrangements, in particular for certain natural quotients of the pure braid group associated with finite graphs, called graphic arrangement groups. This is based on a joint paper with Dan Cohen and Dick Randell, and work in progress with Cohen.
In the second half of the talk we will describe a recent result establishing a classification of graphic arrangement groups via matroid theory, work in progress with Geoff Whittle.