A Note on Fine Graphs and Homological Isoperimetric Inequalities
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 170-181
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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.
Mots-clés :
20F67, 05C10, 20J05, 57M60, isoperimetric functions, Dehn functions, hyperbolic groups
Martínez-Pedroza, Eduardo. A Note on Fine Graphs and Homological Isoperimetric Inequalities. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 170-181. doi: 10.4153/CMB-2015-070-2
@article{10_4153_CMB_2015_070_2,
author = {Mart{\'\i}nez-Pedroza, Eduardo},
title = {A {Note} on {Fine} {Graphs} and {Homological} {Isoperimetric} {Inequalities}},
journal = {Canadian mathematical bulletin},
pages = {170--181},
year = {2016},
volume = {59},
number = {1},
doi = {10.4153/CMB-2015-070-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-070-2/}
}
TY - JOUR AU - Martínez-Pedroza, Eduardo TI - A Note on Fine Graphs and Homological Isoperimetric Inequalities JO - Canadian mathematical bulletin PY - 2016 SP - 170 EP - 181 VL - 59 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-070-2/ DO - 10.4153/CMB-2015-070-2 ID - 10_4153_CMB_2015_070_2 ER -
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