Introducing geodesic currents, Bonahon described a pairing I: T(S) x
T(S) -> R on the Teichmüller space T(S) of a closed surface S. We
consider a natural generalization to a pairing J : QF(S) x QF(S) -> R
on quasifuchsian space QF(S). By naturality, it follows that the
extended mapping class group of the surface S preserves J. We prove
that the group of maps that preserve J not only contains, but is equal
to the extended mapping class group of the surface. This is joint work
with R. Canary.