The 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 geometric techniques to prove algebraic properties for large classes of groups.
Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems.
Infinite groups, Transformation groups Hyperbolic manifolds, groups and actions, Ann. Math. Studies 97 (1981), 183-215, Princeton University Press, Princeton. Groups of polynomial growth and expanding maps.
Geometric ideas have played a very major role in the development of Group theory in 20th century. Coxeter groups and Coxeter complexes, Tits theory of buildings, Bass-Serre theory of Groups acting on trees, Gromov’s notion of hyperbolic groups and combinatorial methods have all been very central in several areas of mathe-matics.
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 More
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.Learn More
In 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 More
Boundaries 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.Learn More
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HYPERBOLIC GROUPS Essay MASt in Pure Mathematics Supervisor: Henry Wilton Cambridge, 4 May 2018.Learn More
The 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 More
The 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 More
X 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 More
This 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 More
The 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 More
In 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 ().Learn More