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Pré-Publication, Document De Travail Année : 2023

Automorphisms of relatively hyperbolic groups and the Farrell-Jones Conjecture

Naomi Andrew
  • Fonction : Auteur
  • PersonId : 1342225
Yassine Guerch
  • Fonction : Auteur
  • PersonId : 1342221
Sam Hughes
  • Fonction : Auteur
  • PersonId : 1342222

Résumé

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: (1) FJC for the automorphism group of a one-ended group hyperbolic relative to virtually polycyclic subgroups; (2) 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.
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Dates et versions

hal-04419054 , version 1 (26-01-2024)

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Naomi Andrew, Yassine Guerch, Sam Hughes. Automorphisms of relatively hyperbolic groups and the Farrell-Jones Conjecture. 2024. ⟨hal-04419054⟩
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