  We construct an invariant called guts for second homology classes in
irreducible 3-manifolds with toral boundary and non-degenerate Thurston norm.
We prove that the guts of second homology classes in each Thurston cone are
invariant under a natural condition. We show that the guts of different
homology classes are related by sutured decompositions. As an application, an
invariant of knot complements is given and is computed in a few interesting
cases. Besides, we show that the dimension of a maximal simplex in a Kakimizu
Complex is an invariant.
