Thurston's norm revisited

Abstract

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.