Let G be a torsion-free hyperbolic group and α an automorphism of G. We show that there exists a canonical collection of subgroups that are polynomially growing under α, and that the mapping torus of G by α is hyperbolic relative to the suspensions of the maximal polynomially growing subgroups under α. As a consequence, we obtain a dichotomy for growth: given an automorphism of a torsion-free hyperbolic group, the conjugacy class of an element either grows polynomially under the automorphism, or at least exponentially.
1
Université Grenoble Alpes, France
2
Tata Institute of Fundamental Research, Mumbai, India; Technion – Israel Institute of Technology, Haifa, Israel
François Dahmani; Suraj Krishna M S. Relative hyperbolicity of hyperbolic-by-cyclic groups. Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 403-426. doi: 10.4171/ggd/703
@article{10_4171_ggd_703,
author = {Fran\c{c}ois Dahmani and Suraj Krishna M S},
title = {Relative hyperbolicity of hyperbolic-by-cyclic groups},
journal = {Groups, geometry, and dynamics},
pages = {403--426},
year = {2023},
volume = {17},
number = {2},
doi = {10.4171/ggd/703},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/703/}
}
TY - JOUR
AU - François Dahmani
AU - Suraj Krishna M S
TI - Relative hyperbolicity of hyperbolic-by-cyclic groups
JO - Groups, geometry, and dynamics
PY - 2023
SP - 403
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UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/703/
DO - 10.4171/ggd/703
ID - 10_4171_ggd_703
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