Aut-invariant quasimorphisms on graph products of abelian groups

2021/07/26 by Bastien Karlhofer, Karlhofer, Bastien
Computer Science · Mathematics · #20E06 (Secondary) #20F65 (Primary) 05C25 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2107.12171

openalex publication_date 2021/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper constructs unbounded quasimorphisms that are invariant under all automorphisms on free products of more than two factors and on graph products of finitely generated abelian groups. This includes many classes of right angled Artin and right angled Coxeter groups. We discuss various geometrically arising families of graphs as examples and deduce the non-triviality of an invariant analogue of stable commutator length recently introduced by Kawasaki and Kimura for these groups.

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• Aut-invariant quasimorphisms on free products
• On property (T) for automorphism groups of graph products
• The automorphism group of a graph product with no SIL
• Automorphisms of graph products of groups and acylindrical hyperbolicity