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Hyperbolic groups, Essays in Group Theory. Hyperbolic groups, Essays in Group Theory / August 28, / Infinite groups. Hyperbolic groups, Essays in Group Theory, S. Gersten ed., MSRI Publications 8 (), Springer. Share this Post. Post navigation.
Abstract: In , Gromov conjectured that for every non-elementary hyperbolic group there is an such that the quotient group is infinite. The article confirms this conjecture. The article confirms this conjecture.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).
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.