Time

Apr 16 2008 - 3:30pm - 4:30 pm

Location

MA 240

Speaker

Matt Day (University of Chicago)

Seminar Website

http://www.math.ohio-state.edu/~sgal/ggt/

Abstract

A right-angled Artin group (RAAG) is a group with a finite resentation whose only relations are commutation relations between
generators. Free groups and free abelian groups are examples of RAAGs but there are many other examples. M. Laurence proved in 1995 that the automorphism group Aut(G) of a RAAG G is finitely generated. This talk addresses the following question: if G is a RAAG and g is in G, how can I tell if the stabilizer of g in Aut(G) is finitely generated? If G is a free group, such a stabilizer is always finitely generated, as a corollary to the classical peak-reduction theorem of J.H.C. Whitehead. I will discuss generalizations of Whitehead's theorem to an arbitrary RAAG.