A Note on Fine Graphs and Homological Isoperimetric Inequalities

Canadian mathematical bulletin

Eduardo Martínez-Pedroza¹ 

[1] Memorial University, St. John's, Newfoundland A1C 5S7

关键词: isoperimetric functions;    Dehn functions;    hyperbolic groups;   

DOI  :  10.4153/CMB-2015-070-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In the framework of homological characterizations of relative hyperbolicity, Groves and Manning posed the question of whether a simply connected $2$-complex $X$ with a linear homological isoperimetric inequality, a bound on the length of attaching maps of $2$-cells and finitely many $2$-cells adjacent to any edge must have a fine $1$-skeleton. We provide a positive answer to this question. We revisit a homological characterization of relative hyperbolicity, and show that a group $G$ is hyperbolic relative to a collection of subgroups $mathcal P$ if and only if $G$ acts cocompactly with finite edge stabilizers on an connected $2$-dimensional cell complex with a linear homological isoperimetric inequality and $mathcal P$ is a collection of representatives ofconjugacy classes of vertex stabilizers.

【 授权许可】

Unknown