曲线图的渐近维数有限
几何拓扑
2014-02-26 v4 群论
摘要
我们对满足 Bowditch 所研究某一有界性条件的双曲度量空间的渐近维数给出了一个上界。主要例子是紧致可定向曲面曲线图上的一族紧密测地线。我们利用此结论得出曲线图具有有限渐近维数。进而可知曲线图具有性质 。我们还计算了亏格 的可定向曲面映射类群的渐近维数。
引用
@article{arxiv.math/0509216,
title = {The asymptotic dimension of a curve graph is finite},
author = {Gregory Bell and Koji Fujiwara},
journal= {arXiv preprint arXiv:math/0509216},
year = {2014}
}
备注
19 pages. Made some minor revisions. The section on mapping class groups has been rewritten; in particular we compute the asdim of Mod(S) where S has genus at most 2. The last section on open questions has been modified to reflect recent developments. References have been updated