映射类群子群的一致一致指数增长
几何拓扑
2009-10-04 v5
摘要
设 Mod(S) 表示紧致可定向曲面 S 的映射类群。我们证明，Mod(S) 中非虚阿贝尔的有限生成子群具有一致指数增长，其最小增长率有一个仅依赖于 S 且必然依赖于 S 的常数下界。在证明中，我们在任何此类子群中找到了显式的自由群生成元，这些生成元在任何字度量下都是“短”的。除了界定增长外，这还允许对简单随机游走的返回概率进行界定。
引用
@article{arxiv.0805.0133,
title = {Uniform uniform exponential growth of subgroups of the mapping class group},
author = {Johanna Mangahas},
journal= {arXiv preprint arXiv:0805.0133},
year = {2009}
}
备注
12 pgs. V5 benefits from referee comments: clearer proof and added reference for Sec. 4; numerical correction in Lemma 2.5 and where it is applied; typos fixed. V4 adds Sec. 4 (growth bound must depend on surface); V3 adds random walks corollary; V2 states stronger result implicit in original proof and corrects formula for growth rate bound