Every real tree is a hyperbolic metric space; moreover, every real tree is 0 hyperbolic.
The Cayley graph of any free group is considered to be a real tree. Note that its graph is a tree in the graph theoretic sense. To make it a real tree, we view the edges as isometric (http://planetmath.org/Isometric) to the line segment under a (surjective) isometry (http://planetmath.org/Isometry) and attach the edges to the tree. The resulting 1-complex is then a locally finite real tree. Because of this result, every free group is a hyperbolic group.
|Date of creation||2013-03-22 15:16:55|
|Last modified on||2013-03-22 15:16:55|
|Last modified by||GrafZahl (9234)|