A Note on Fine Graphs and Homological Isoperimetric Inequalities
A Note on Fine Graphs and Homological Isoperimetric Inequalities
复制标题
关于精细图和同调等周不等式的注记
DOI：
10.4153/cmb-2015-070-2
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Eduardo Martínez
中科院分区：
文献类型：
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作者：
Eduardo Martínez
在相对双曲性的同调刻画框架下，Groves和Manning提出了这样一个问题：具有线性同调等周不等式的单连通2-复数$X$，2-胞格的附着映射的长度的界，以及任意边相邻的有限多个2-胞格是否一定有精细的1-骨架。我们对这个问题给出了肯定的回答。我们重温了相对双曲性的一个同调刻划，证明了群$G是相对于子群集合$P$的双曲群当且仅当$G$与具有线性同调等周不等式的连通2维胞复形上的有限边稳定子协紧作用，且$P$是顶点稳定子的共轭类的代表的集合.
Abstract 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 attachingmaps 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 $P$ if and only if $G$ acts cocompactly with finite edge stabilizers on a connected 2-dimensional cell complex with a linear homological isoperimetric inequality and $P$ is a collection of representatives of conjugacy classes of vertex stabilizers.