Between Tits buildings and free factor complexes

Vortrag von Dr. Benjamin Brück

Datum: 28.10.20  Zeit: 16.15 - 17.15  Raum: ETH HG G 19.1

Much of the modern treatment of automorphism groups of free groups is motivated by analogies with arithmetic groups. I will present a new family of simplicial 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 the new complexes is associated to the automorphism group Aut(A_\Gamma) 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_\Gamma). These complexes can also be seen as an Aut(A_\Gamma)-​analogue of the curve complex.