有限生成群及其子群的渐近维数与 Assouad-Nagata 维数
群论
2020-10-09 v1 度量几何
摘要
我们证明：对所有满足 的 ，存在一个有限生成群 及其有限生成子群 ，使得 的渐近维数为 ， 的 Assouad-Nagata 维数为 ，且 的 Assouad-Nagata 维数为 。这同时回答了渐近维数理论中的两个公开问题。
引用
@article{arxiv.2010.03709,
title = {Asymptotic and Assouad-Nagata dimension of finitely generated groups and their subgroups},
author = {Levi Sledd},
journal= {arXiv preprint arXiv:2010.03709},
year = {2020}
}
备注
33 pages, 7 figures This paper is a sequel to "Assouad-Nagata dimension of C'(1/6) groups" (1909.06646). Some of the results from the previous paper have been shifted to this one, since their proofs use similar techniques. The author believes this reorganization will make both papers easier to read and greatly reduce their combined length