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For the free group FN of finite rank N ≥ 2 we construct a canonical Bonahon-type, continuous and Out(FN)-invariant geometric intersection form , : cv(FN) × Curr(FN) → R ≥0. Here cv(FN) is the closure of unprojectivized Culler-Vogtmann's Outer space cv(FN) in the equivariant Gromov-Hausdorff convergence topol-ogy (or, equivalently, in the length function(More)
A geodesic lamination L on a hyperbolic surface S, provided with a transverse measure, defines (via the lift L of L to the universal covering of S) an action of π 1 S on an R-tree T which is often called dual to the lamination L. Conversely, every small action of π 1 S on an R-tree T comes from this construction, provided the surface is closed and the(More)
A geodesic lamination L on a closed hyperbolic surface S, when provided with a transverse measure µ, gives rise to a " dual R-tree " T µ , together with an action of G = π 1 S on T µ by isometries. A point of T µ corresponds precisely to a leaf of the lift L of L to the universal covering S of S, or to a complementary component of L in S. The G-action on T(More)
We show that every automorphism α of a free group F k of finite rank k has asymptotically periodic dynamics on F k and its boundary ∂F k : there exists a positive power α q such that every element of the compactum F k ∪ ∂F k converges to a fixed point under iteration of α q. Further results about the dynamics of α as well as an extension from F k to(More)
Let T be an R-tree with a very small action of a free group F N which has dense orbits. Such a tree T or its metric completion T are not locally compact. However, if one adds the Gromov boundary ∂T to T , then there is a coarser observers' topology on the union T ∪ ∂T , and it is shown here that this union, provided with the observers' topology, is a(More)
In this paper we show that for a given 3-manifold and a given Hee-gaard splitting there are finitely many preferred decomposing systems of 3g − 3 disjoint essential disks. These are characterized by a combi-natorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist(More)