For the free group FNβ of finite rank Nβ₯2 we construct a canonical
Bonahon-type continuous and Out(FNβ)-invariant \emph{geometric intersection
form} :cvΛ(FNβ)ΓCurr(FNβ)βRβ₯0β.
Here cvΛ(FNβ) is the closure of unprojectivized Culler-Vogtmann's
Outer space cv(FNβ) in the equivariant Gromov-Hausdorff convergence topology
(or, equivalently, in the length function topology). It is known that
cvΛ(FNβ) consists of all \emph{very small} minimal isometric actions of
FNβ on R-trees. The projectivization of cvΛ(FNβ) provides a
free group analogue of Thurston's compactification of the Teichm\"uller space.
As an application, using the \emph{intersection graph} determined by the
intersection form, we show that several natural analogues of the curve complex
in the free group context have infinite diameter.Comment: Revised version, to appear in Geometry & Topolog