Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:actsOn |
gptkb:CAT(0)_space
|
| gptkbp:citation |
Bridson, Martin R.; Haefliger, André. Metric Spaces of Non-Positive Curvature (1999)
Gromov, Mikhael. Hyperbolic Groups (1987) Davis, Michael W. The Geometry and Topology of Coxeter Groups (2008) |
| gptkbp:defines |
groups that act geometrically (properly discontinuously, cocompactly, by isometries) on a CAT(0) space
|
| gptkbp:example |
gptkb:Coxeter_groups
fundamental groups of non-positively curved manifolds free abelian groups right-angled Artin groups |
| gptkbp:field |
geometric group theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
CAT(0) groups
|
| gptkbp:introduced |
gptkb:Mikhael_Gromov
|
| gptkbp:openProblem |
Does every CAT(0) group have a finite-index subgroup with trivial center?
Does every CAT(0) group have a finite-index subgroup that splits as a direct product? |
| gptkbp:property |
CAT(0) groups are finitely presented
CAT(0) groups have solvable conjugacy problem CAT(0) groups have solvable word problem CAT(0) groups satisfy the Tits alternative every hyperbolic group is a CAT(0) group not every CAT(0) group is hyperbolic torsion-free CAT(0) groups have finite cohomological dimension |
| gptkbp:relatedTo |
gptkb:hyperbolic_groups
non-positive curvature cube complexes |
| gptkbp:bfsParent |
gptkb:Farrell–Jones_conjecture
|
| gptkbp:bfsLayer |
6
|