A Tits alternative for rational functions
Number Theory
2021-03-19 v1 Algebraic Geometry
Group Theory
Abstract
We prove an analog of the Tits alternative for rational functions. In particular, we show that if is a finitely generated semigroup of rational functions over the complex numbers, then either has polynomially bounded growth or contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field that do not have the same set of preperiodic points, then the semigroup generated by f and g contains a nonabelian free semigroup.
Cite
@article{arxiv.2103.09994,
title = {A Tits alternative for rational functions},
author = {Jason P. Bell and Keping Huang and Wayne Peng and Thomas J. Tucker},
journal= {arXiv preprint arXiv:2103.09994},
year = {2021}
}
Comments
16 pages