  We study the Thurston norm on the second homology of a 3-manifold M, which is
the surface bundle over the circle with a pseudo-Anosov monodromy. A novelty of
our approach consists in the application of the C*-algebras to a problem in
topology. Namely, one associates to M a C*-algebra, whose K-theory gives rise
to an algebraic number field K. It is shown, that the trace function on the
ring of integers of K induces a norm on the second homology of M. The norm
coincides with the Thurston norm on the second homology of M.
