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Gromov introduced geometric group theory, the study of infinite groups via the geometry of their Cayley graphs and their word metric. In 1981 he proved Gromov's theorem on groups of polynomial growth: a finitely generated group has polynomial growth (a geometric property) if and only if it is virtually nilpotent (an algebraic property).

Learn MoreIn 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.

Learn MoreIn group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.

Learn MoreBoundaries of Gromov hyperbolic groups and visual metrics Quasi-conformal and quasi-Mobius maps on metric spaces References No textbook is required, but here are some helpful references. Books: Mikhail Gromov, Hyperbolic Groups, pp.75-263, Essays in group theory, Springer, 1987.

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Learn MoreHYPERBOLIC GROUPS Essay MASt in Pure Mathematics Supervisor: Henry Wilton Cambridge, 4 May 2018.

Learn MoreThe subject matter is hyperbolic groups - one of the main objects of study in geometric group theory. Geometric group theory began in the 1980's with work of Cannon, Gromov and others, applying.

Learn MoreThe asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.

Learn MoreX is Gromov-hyperbolic, which corresponds to negative curvature. Then we study the case when X is CAT(0), which corresponds to non-positive curvature. In order for this theory to be useful, we need a rich supply of negatively and non-positively curved spaces. We develop the theory of non-positively curved cube complexes, which.

Learn MoreThis is a hyperbolic group whose Gromov boundary is a Cantor set. Hyperbolic groups and their boundaries are important topics in geometric group theory, as are Cayley graphs.

Learn MoreThe theory of hyperbolic spaces was introduced by M. Gromov in (1, 2),. the study of Gromov hyperbolic graphs can shed light on the.. as hyperbolic groups have a soluble.

Learn MoreIn group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.The notion of a hyperbolic group was introduced and developed by Mikhail Gromov ().

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