Fixed subgroups of automorphisms of RAAGs

Meeting ID: 931 7291 0947
For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

If G is the fundamental group of a closed surface, standard Nielsen-Thurston theory shows that fixed subgroups of automorphisms of G are either trivial, infinite cyclic, or fundamental groups of subsurfaces. In sharp contrast, understanding automorphisms of free groups and their fixed points has proved a much more arduous task, being the subject of a large body of work in the 70s and 80s before being completely resolved by Bestvina and Handel in the early 90s. Comparatively little attention has been given to automorphisms of other groups. Aiming to fill this gap, we study a large class of non-positively curved groups containing all right-angled Artin and Coxeter groups and show that all their "untwisted" automorphisms have particularly nice fixed subgroups: they are finitely generated, quasi-isometrically embedded, and admit finite classifying spaces of non-positive curvature.