an:01342230
Zbl 0952.20032
Bowditch, B. H.
Convergence groups and configuration spaces
EN
Cossey, John (ed.) et al., Geometric group theory down under. Proceedings of a special year in geometric group theory, Canberra, Australia, July 14-19, 1996. Berlin: de Gruyter. 23-54 (1999).
1999
a
20F65 57M60 57M07 20F67 54F50
convergence groups; compact Hausdorff spaces; conformal actions; word hyperbolic groups
The paper develops some of the basic properties of convergence groups (initially introduced by \textit{F.~W.~Gehring} and \textit{G.~J.~Martin} [Lect. Notes Math. 1275, 158-167 (1987; Zbl 0623.30030)]) in the fairly general context of an arbitrary compact Hausdorff space, from the point of view of the induced action on the space of distinct triples. This view is equivalent to the original Gehring-Martin definition in the case of topological spheres -- it axiomatises the essential dynamical properties of a discrete conformal action on the ideal sphere of real hyperbolic space, see the reviewer's book [Conformal geometry of discrete groups and manifolds, Walter de Gruyter (2000)]. The motivation of this generalization stems from the fact that a word hyperbolic group (in the sense of Gromov) acting on its boundary satisfies the convergence axioms.
For the entire collection see [Zbl 0910.00040].
Boris N.Apanasov (Norman)
Zbl 0623.30030