Explore: Hyperbolic Groups And Nonpositively Curved Groups

Discrete subgroups of Lie groups. Springer-Verlag. Margulis, Grigori (1975). "Discrete groups of motions of manifolds of nonpositive curvature". Proceedings

E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used

nonpositive sectional curvature. For example, SL(2,R)/SO(2) is the hyperbolic plane, and SL(2,C)/SU(2) is hyperbolic 3-space. For a reductive group G

Gromov-hyperbolic groups and their generalizations (relatively and acylindrically hyperbolic groups), free groups and their automorphisms, groups acting

detail by Burago, Gromov and Perelman in 1992.[BGP92] Along with Eliyahu Rips, Gromov introduced the notion of hyperbolic groups.[G87] Gromov's theory of

construction of Kac–Moody groups in algebra, and to nonpositively curved manifolds and hyperbolic groups in topology and geometric group theory. Buekenhout geometry

Consequently, its fundamental group Γ = π1(M) is Gromov hyperbolic. This has many implications for the structure of the fundamental group: it is finitely presented;

Bestvina and Feighn, 1992; general case: Brinkmann, 2000). Hyperbolic free-by-cyclic groups are fundamental groups of compact non-positively curved cube complexes

discrete subgroups of isometries of a non-positively curved Riemannian manifold (e.g. the hyperbolic n-space). Roughly, it states that within a fixed radius

referred to as Euclidean and hyperbolic respectively. The characteristic features of the geometry of non-positively curved Riemann surfaces are used