Geometric group theory

graph whose vertices and edges represent the elements of a group and their products with the generators of the group

free object in the category of groups; a group admitting a presentation without any relations

area in mathematics devoted to the study of finitely generated groups

discrete subgroup of a topological group G is a subgroup H such that there is an open cover of H in which every open subset contains exactly one element of H; in other words, the subspace topology of H in G is the discrete topology

thumb|alt=A hexaflexagon, shown with the same face in two configurations|A hexaflexagon, shown with the same face in two configurations In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.

locally compact topological group admitting a left- or right-invariant mean

parametrizes complex structures on a surface

Mathematical concept

Group realized geometrically by reflections across the sides of a triangle

In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale details. Two metric spaces are quasi-isometric if there exists a quasi-isometry between them. The property of being quasi-isometric behaves like an equivalence relation on the class of metric spaces.

mathematical structure

important theorem about the structure of finitely generated linear groups

disproved conjecture in group theory

way to measure distance between any two elements of group (in group theory)

theorem in geometric group theory

lemma in geometric group theory, giving sufficient conditions for when a group equipped with an isometric action on a metric space is quasi-isometric to the metric space