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On the Asymptotic Homological Dimension of Hyperbolic Groups
Author(s) -
Światkowski Jacek
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.3.209
Subject(s) - mathematics , hyperbolic group , isoperimetric inequality , pure mathematics , relatively hyperbolic group , dimension (graph theory) , invariant (physics) , hyperbolic space , group (periodic table) , hyperbolic manifold , mathematical analysis , hyperbolic function , chemistry , organic chemistry , mathematical physics
We introduce the notion of asymptotic homological dimension asdim h of a metric space (invariant under quasiisometry), and show that dim∂ ∞ Г +1 ⩽ asdim h Г ⩽ asdim + Г for a (word‐)hyperbolic group Г (asdim + is the large‐scale dimension defined by M. Gromov). We show also that asdim h Г ⩽2 for a certain class of hyperbolic groups (introduced by M. Gromov) that we call strongly isoperimetric groups.