Automorphisms of virtually special groups

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• Elia Fioravanti (Karlsruhe Institute of Technology (KIT))
• Monday 01 September 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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OGGW02 - Actions on graphs and metric spaces

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 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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