Automorphisms of virtually special groupsGeometric Group Theory Oberseminar

by Dr Elia Fioravanti (KIT)

Wednesday Oct 22, 2025, 11:00 AM → 12:00 PM Europe/Berlin

Endenicher Allee 60/0-008 (Mathezentrum)

For which families of finitely generated groups G are automorphisms "tame"? For instance, one can wonder whether Out(G) is finitely generated, or whether the stretch factors of the automorphisms of G are algebraic integers. Following breakthroughs of Rips and Sela in the 90s, automorphisms of hyperbolic groups are known to satisfy both of these forms of tameness, but much less is known on automorphisms of more general non-positively curved groups. We show that automorphisms of compact special groups (in the sense of Haglund and Wise) also satisfy the same two forms of tameness. Proofs rely on non-small R-trees and a new JSJ decomposition over centralisers.