Automorphisms of relatively hyperbolic groups and the Farrell–Jones conjecture

Journal article

We prove the fibred Farrell–Jones conjecture (FJC) in A-, K-, and L-theory for a large class of suspensions of relatively hyperbolic groups, as well as for all suspensions of one-ended hyperbolic groups. We deduce two applications: FJC for the automorphism group of a one-ended group hyperbolic relative to virtually polycyclic subgroups; FJC is closed under extensions of FJC groups with kernel in a large class of relatively hyperbolic groups. Along the way we prove a number of results about JSJ decompositions of relatively hyperbolic groups which may be of independent interest.

Authors: Andrew, N; Guerch, Y; Hughes, S

• Alternative title: Automorphisms of relatively hyperbolic groups and the Farrell–Jones..
• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Mathematische Annalen
• Volume: 395
• Issue: 4
• Article number: 89
• Publication date: 2026-06-16
• Acceptance date: 2026-03-01
• DOI: 10.1007/s00208-026-03431-7
• EISSN: 1432-1807
• ISSN: 0025-5831
• Language: English
• Keywords: 20F65; 20E08; Secondary 20F28; Primary 18F25; 20F67