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A small simplification in hyperbolic groups. (Petite simplification dans les groupes hyperboliques.) (French) Zbl 0803.53026
Summary: In this paper, we give a complete proof of the statement of M. Gromov that the quotient of any hyperbolic group by elements which satisfy some “small cancellation” property is still hyperbolic. This leads us to define a notion of volume in general metric spaces and, following M. Gromov, to study properties of the geodesic flow acting on hyperbolic groups, as compared to the case of negatively curved manifolds.

MSC:
53C20 Global Riemannian geometry, including pinching
57M05 Fundamental group, presentations, free differential calculus
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
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