Polynomial invariants for fibered 3-manifolds and Teichmuller geodesics for foliations

Let F subset of H-1(M-3, R) be a fibered face of the Thurston norm bail for a hyperbolic 3-manifold M. Any phi epsilon R+. F determines a measured foliation F of M. Generalizing the case of Teichmuller geodesics and fibrations, we show F carries a canon ical Riemann surface structure on its leaves, and a transverse Teichmuller flow with pseudo-Anosov expansion factor K(phi) > 1. We introduce a polynomial invariant Theta(F) epsilon Z[H-1(M, Z)/torsion] w hose roots determine K(phi). The Newton polygon of Theta(F) allows one to c ompute fibered faces in practice, as we illustrate for closed braids in S-3 . Using fibrations we also obtain a simple proof that the shortest geodesic on moduli space M, has length O(1/g). (C) 2000 Editions scientifiques et m edicales Elsevier SAS.