Canadian mathematical bulletin | |
A Note on Fine Graphs and Homological Isoperimetric Inequalities | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912050577188ZK.pdf | 18KB | download |