  We give a proof of the Gap Labeling Conjecture formulated by J. Bellissard.
This gives information about the spectrum of a Schrodinger operator associated
to a quasicrystal. The proof makes use of a version of Connes' Index Theorem
for Foliations which was introduced by C. Moore and C. Schochet and is
appropriate for foliated spaces. These arise naturally in dynamics and are
likely to have further applications.
