Automorphisms of relatively hyperbolic groups and the Farrell--Jones Conjecture
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912935273562112 |
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| author | Andrew, Naomi Guerch, Yassine Hughes, Sam |
| author_facet | Andrew, Naomi Guerch, Yassine Hughes, Sam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14036 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automorphisms of relatively hyperbolic groups and the Farrell--Jones Conjecture Andrew, Naomi Guerch, Yassine Hughes, Sam K-Theory and Homology Algebraic Topology Group Theory Geometric Topology 18F25 (Primary) 20F28, 20F65, 20F67, 20E08 (Secondary) 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. |
| title | Automorphisms of relatively hyperbolic groups and the Farrell--Jones Conjecture |
| topic | K-Theory and Homology Algebraic Topology Group Theory Geometric Topology 18F25 (Primary) 20F28, 20F65, 20F67, 20E08 (Secondary) |
| url | https://arxiv.org/abs/2311.14036 |