Volume 8 of the series Mathematical Sciences Research Institute Publications pp 75263
Hyperbolic Groups
 M. GromovAffiliated withIHES
Abstract
Let us start with three equivalent definitions of hyperbolic groups. First observe that for every finitely presented group Γ there exists a smooth bounded (i.e. bounded by a smooth hypersurface) connected domain V ⊂ ℝ^{n} for every n ≥ 5. such that the fundamental group π_{1}(V) is isomorphic to Γ. A standard example of such a V is obtained as follows. Fix a finite presentation of Γ and let P be the 2dimensional cell complex whose 1cells correspond in the usual way to the generators and the 2cells to the relations in Γ, such that π_{1}(P) = Γ. Then embed P into ℝ^{5} and take a regular neighborhood of P ⊂ ℝ^{5} for V.
 Title
 Hyperbolic Groups
 Book Title
 Essays in Group Theory
 Pages
 pp 75263
 Copyright
 1987
 DOI
 10.1007/9781461395867_3
 Print ISBN
 9781461395881
 Online ISBN
 9781461395867
 Series Title
 Mathematical Sciences Research Institute Publications
 Series Volume
 8
 Series ISSN
 09404740
 Publisher
 Springer New York
 Copyright Holder
 SpringerVerlag New York Inc.
 Additional Links
 Topics
 Industry Sectors
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 Editors

 S. M. Gersten ^{(1)}
 Editor Affiliations

 1. Department of Mathematics, University of Utah
 Authors

 M. Gromov ^{(2)}
 Author Affiliations

 2. IHES, France
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