High Quality Content by WIKIPEDIA articles! In group theory, a
hyperbolic group, also known as a word hyperbolic group, Gromov
hyperbolic group, negatively curved group is a finitely generated
group equipped with a word metric satisfying certain properties
characteristic of hyperbolic geometry. The notion of a hyperbolic
group was introduced and developed by Mikhail Gromov in the early
1980s. He noticed that many results of Max Dehn concerning the
fundamental group of a hyperbolic Riemann surface do not rely
either on it having dimension two or even on being a manifold and
hold in much more general context. In a very influential paper from
1987, Gromov proposed a wide-ranging research program. Ideas and
foundational material in the theory of hyperbolic groups also stem
from the work of George Mostow, William Thurston, James W. Cannon,
Eliyahu Rips, and many others.
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