We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Relative hyperbolicity of free-by-cyclic extensions.
- Authors
Ghosh, Pritam
- Abstract
Given a finitely generated free group $ {\mathbb {F} }$ of $\mathsf {rank}({\mathbb {F} })\geq 3$ , we show that the mapping torus of $\phi$ is (strongly) relatively hyperbolic if $\phi$ is exponentially growing. As a corollary of our work, we give a new proof of Brinkmann's theorem which proves that the mapping torus of an atoroidal outer automorphism is hyperbolic. We also give a new proof of the Bridson–Groves theorem that the mapping torus of a free group automorphism satisfies the quadratic isoperimetric inequality. Our work also solves a problem posed by Minasyan and Osin: the mapping torus of an outer automorphism is not virtually acylindrically hyperbolic if and only if $\phi$ has finite order.
- Subjects
ISOPERIMETRIC inequalities; AUTOMORPHISM groups; FREE groups; TORUS
- Publication
Compositio Mathematica, 2023, Vol 159, Issue 1, p153
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X22007813