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Non-uniform exponential growth and the decay of growth rates in growing dimensions
Abstract
We provide the first example of a finitely presented, and the first example of a simple, group of non-uniform exponential growth. The example is given by Thompson's group V. Our methods also show that the infimal exponential growth rates of Aut(F2n+2) and of EL2n+2(R), for every finitely generated ring R, tend to $1$. As an application, we obtain the first example of an acylindrically hyperbolic group, and the first example of a Kazhdan group, of non-uniform exponential growth.
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BibTeX
@misc{sauer2026nonuniform,
title = {{Non-uniform exponential growth and the decay of growth rates in growing dimensions}},
author = {Roman Sauer and Eduard Schesler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.30163},
eprint = {2605.30163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30163},
}
RIS
TY - UNPB
TI - Non-uniform exponential growth and the decay of growth rates in growing dimensions
AU - Roman Sauer
AU - Eduard Schesler
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2605.30163
UR - https://arxiv.org/abs/2605.30163
AB - We provide the first example of a finitely presented, and the first example of a simple, group of non-uniform exponential growth. The example is given by Thompson's group V. Our methods also show that the infimal exponential growth rates of Aut(F_2^n+2) and of EL_2^n+2(R), for every finitely generated ring R, tend to $1$. As an application, we obtain the first example of an acylindrically hyperbolic group, and the first example of a Kazhdan group, of non-uniform exponential growth.
ER -