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Geodesic currents on negatively curved groups. (English) Zbl 0772.57004
Arboreal group theory, Proc. Workshop, Berkeley/CA (USA) 1988, Publ., Math. Sci. Res. Inst. 19, 143-168 (1991).
[For the entire collection see Zbl 0744.00026.]
The author’s abstract: “A negatively curved or hyperbolic group, as introduced by M. Gromov, is a finitely generated group whose Cayley graphs asymptotically behave at infinity like a tree. Considering the actions of a negatively curved group on one of its Cayley graphs, we study asymptotic directions in the set of conjugacy classes of this group. We then discuss some applications to group actions on $$\mathbb{R}$$- trees and manifolds of negative curvature”.

##### MSC:
 57M15 Relations of low-dimensional topology with graph theory
##### Keywords:
negatively curved; hyperbolic group; Cayley graphs; tree