群的维数增长
群论
2012-07-25 v4 代数拓扑
组合数学
摘要
群的维数增长函数由Gromov于1999年引入。我们证明了R. Thompson群的每个可解有限生成子群具有多项式维数增长，而群本身以及某些3类可解群具有指数维数增长且指数可控。我们描述了维数增长、有限图的扩张性质与Ramsey理论之间的联系。
引用
@article{arxiv.1008.3868,
title = {On the dimension growth of groups},
author = {Alexander Dranishnikov and Mark Sapir},
journal= {arXiv preprint arXiv:1008.3868},
year = {2012}
}
备注
20 pages; v3: Erratum and addendum included as Section 9. We can only prove that the lower bound of the dimension growth of $F$ is exp sqrt(n). New open questions and comments are added. v4: The paper is completely revised. Dimension growth with control is introduced, connections with graph expansion and Ramsey theory are included