A note on fine graphs and homological isoperimetric inequalities
| Autor: | Eduardo Martínez-Pedroza |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Vertex (graph theory)
Pure mathematics Inequality Cell complex General Mathematics media_common.quotation_subject Group Theory (math.GR) 0102 computer and information sciences Characterization (mathematics) 01 natural sciences Mathematics - Geometric Topology Conjugacy class Simply connected space FOS: Mathematics Mathematics - Combinatorics 20F67 05C10 20J05 57M60 0101 mathematics media_common Mathematics Group (mathematics) 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology 010201 computation theory & mathematics Combinatorics (math.CO) Isoperimetric inequality Mathematics - Group Theory |
| Popis: | 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 of conjugacy classes of vertex stabilizers. Version accepted by the Canadian Mathematical Bulletin |
| Databáze: | OpenAIRE |
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