Algebra/Topology Seminar

Speaker:  Benjamin Brück (Bielefeld University)

Title: Between Tits buildings and free factor complexes

Abstract:

Much of the modern treatment of automorphism groups of free groups is motivated by analogies with arithmetic groups –  this is especially true if it comes to homological questions. I will present a new family of complexes interpolating between two well-studied objects associated to these classes of groups: the free factor complex  and the Tits building of GL_n(Q). Each of these new complexes is associated to the automorphism group Aut(A_Γ) of a right-angled Artin group and has the homotopy type of a wedge of spheres. The dimension of these spheres forms a new invariant associated to Aut(A_Γ).