Intersection form, laminations and currents on free groups

الأصل · EN

Let Fₙ be a free group of rank N≥ 2, let μ be a geodesic current on Fₙ and let T be an R-tree with a very small isometric action of Fₙ. We prove that the geometric intersection number <T, μ> is equal to zero if and only if the support of μ is contained in the dual algebraic lamination L²(T) of T. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a filling element in Fₙ and prove that filling elements are "nearly generic" in Fₙ. We also apply our results to the notion of bounded translation equivalence in free groups.