Statements (48)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
Gromov-hyperbolic groups
|
| gptkbp:application |
dynamics
low-dimensional topology algorithmic group theory |
| gptkbp:characterizedBy |
linear isoperimetric inequality
negative curvature properties slim triangles property |
| gptkbp:example |
infinite cyclic group
abelian group of rank greater than 1 free group of rank at least 2 fundamental group of a closed hyperbolic surface fundamental group of a hyperbolic 3-manifold |
| gptkbp:field |
geometric group theory
group theory |
| gptkbp:generalizes |
free groups
relatively hyperbolic groups |
| gptkbp:hasInvariant |
gptkb:Gromov_boundary
|
| gptkbp:hasProperty |
finite presentation
coarse negative curvature finite asymptotic dimension linear Dehn function no Baumslag–Solitar subgroups no infinite torsion subgroup residually finite (in many cases) solvable conjugacy problem solvable isomorphism problem strong Tits alternative virtually torsion-free finite number of conjugacy classes of finite subgroups finite outer automorphism group (if torsion-free and non-elementary) |
| https://www.w3.org/2000/01/rdf-schema#label |
hyperbolic groups
|
| gptkbp:introduced |
gptkb:Mikhael_Gromov
|
| gptkbp:introducedIn |
1987
|
| gptkbp:property |
exponential growth
finitely generated automatic group boundary at infinity finite presentation solvable word problem |
| gptkbp:relatedTo |
gptkb:Weyl_group
free groups delta-hyperbolicity fundamental group of closed hyperbolic manifolds word metric |
| gptkbp:studiedIn |
Gromov's 1987 paper 'Hyperbolic groups'
|
| gptkbp:bfsParent |
gptkb:Farrell–Jones_conjecture
|
| gptkbp:bfsLayer |
6
|