论调和函数与 Gromov 定理的线性增长情形
群论
2013-11-20 v3 组合数学
度量几何
摘要
我们证明，有限生成无限群 G 上的调和函数空间是有限维的，当且仅当 G 拥有一个同构于整数群的有限指数子群。一个关键工具是 Wilkie 和 van den Dries 关于多项式增长群的 Gromov 定理中线性增长情形的定量版本。
引用
@article{arxiv.1301.1566,
title = {On harmonic functions and the linear-growth case of Gromov's theorem},
author = {Matthew Tointon},
journal= {arXiv preprint arXiv:1301.1566},
year = {2013}
}
备注
This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 3.3. This came to light after an observation made by an anonymous referee, for which the the author is grateful