  Let M be a closed orientable irreducible 3-manifold, and let f be a
diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is
invariant and the induced action of f over \pi_1(T) is hyperbolic. We prove
that only few irreducible 3-manifolds admit Anosov tori: (1) the 3-torus, (2)
the mapping torus of -id, and (3) the mapping torus of hyperbolic automorphisms
of the 2-torus. This has consequences for instance in the context of partially
hyperbolic dynamics of 3-manifolds: if there is an invariant center-unstable
foliation, then it cannot have compact leaves [19]. This has lead to the first
example of a non-dynamically coherent partially hyperbolic diffeomorphism with
one-dimensional center bundle [19].
