平面与平面图的无维渐近维数
度量几何
2021-07-09 v2 组合数学
几何拓扑
摘要
我们证明，同胚于平面中某个子集的测地空间其渐近维数至多为三。特别地，平面及任意平面图的渐近维数至多为三。
引用
@article{arxiv.2002.01630,
title = {Asymptotic dimension of planes and planar graphs},
author = {Koji Fujiwara and Panos Papasoglu},
journal= {arXiv preprint arXiv:2002.01630},
year = {2021}
}
备注
Definitions of M-fat theta curve and M-coarse cactus are slightly changed. The proof of Theorem 3.2 (it used to be Theorem 3.1) is changed and now simpler. Some references are added, in particular [16] by Jorgensen and Lang