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<p>We prove the fibred Farrell–Jones conjecture (FJC) in <i>A</i>-, <i>K</i>-, and <i>L</i>-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: <OrderedList> <ListItem> <ItemNumber>(1)</ItemNumber> <ItemContent> <p>FJC for the automorphism group of a one-ended group hyperbolic relative to virtually polycyclic subgroups;</p> </ItemContent> </ListItem> <ListItem> <ItemNumber>(2)</ItemNumber> <ItemContent> <p>FJC is closed under extensions of FJC groups with kernel in a large class of relatively hyperbolic groups.</p> </ItemContent> </ListItem> </OrderedList> Along the way we prove a number of results about JSJ decompositions of relatively hyperbolic groups which may be of independent interest.</p>

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Automorphisms of relatively hyperbolic groups and the Farrell–Jones conjecture

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月16日

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  • Naomi Andrew,
  • Yassine Guerch,
  • Sam Hughes

摘要

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.