PolExp growth for automorphisms of toral relatively hyperbolic groups
Group Theory
2025-12-08 v1
Abstract
Let be a toral relatively hyperbolic group, and let . We prove that, under iteration of , the conjugacy length of every element grows like for some and some algebraic integer . For a given , only finitely many values of and occur as varies in . The same statements hold for the growth of the word length . For hyperbolic, we generalize polynomial subgroups: we show that, for a given growth type other than , there is a malnormal family of quasiconvex subgroups such that a conjugacy class grows at most like if and only if is conjugate into one of the subgroups .
Cite
@article{arxiv.2512.05569,
title = {PolExp growth for automorphisms of toral relatively hyperbolic groups},
author = {Rémi Coulon and Arnaud Hilion and Camille Horbez and Gilbert Levitt},
journal= {arXiv preprint arXiv:2512.05569},
year = {2025}
}