The Karoubi-Weibel complexity for groups

Autor:	Babenko, Ivan, Moulla, Thiziri
Rok vydání:	2021
Předmět:	Mathematics - Group Theory Mathematics - Geometric Topology 20F65 53C23 G.0
Druh dokumentu:	Working Paper
Popis:	Let $G$ be a finitely presented group. A new complexity called \textit{Karoubi-Weibel complexity} or \textit{covering type}, is defined for $G$. The construction is inspired by recent work of Karoubi and Weibel \cite{KW}, initially applied to topological spaces. We introduce a similar notion in combinatorial form in order to apply it to finitely presentable groups. Some properties of this complexity as well as a few examples of calculation/estimation for certain classes of finitely presentable groups are considered. Finally we give a few applications of complexity to some geometric problems, namely to the systolic area and the volume entropy of groups. Comment: 25 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.00852 Zobrazit plný text záznamu View this record from Arxiv