当前位置: X-MOL 学术Proc. Am. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Poorly connected groups
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-08-14 , DOI: 10.1090/proc/15128
David Hume , John Mackay

Abstract:We investigate groups whose Cayley graphs have poorly connected subgraphs. We prove that a finitely generated group has bounded separation in the sense of Benjamini-Schramm-Timár if and only if it is virtually free. We then prove a gap theorem for connectivity of finitely presented groups, and prove that there is no comparable theorem for all finitely generated groups. Finally, we formulate a connectivity version of the conjecture that every group of type $ F$ with no Baumslag-Solitar subgroup is hyperbolic, and prove it for groups with at most quadratic Dehn function.


中文翻译:

连接不良的群体

摘要:我们调查了Cayley图的子图连接不良的组。我们证明,当且仅当它实际上是自由的时,从Benjamini-Schramm-Timár的意义上说,一个有限生成的群已经限制了分离。然后,我们证明了有限表示的组的连通性的间隙定理,并证明了所有有限生成的组都没有可比的定理。最后,我们建立了猜想的连通性版本,即$ F $没有Baumslag-Solitar子组的每个类型的组都是双曲线的,并针对具有最多二次Dehn函数的组证明了这一关系。
更新日期:2020-09-02
down
wechat
bug