Normal tori in

The fundamental group of M = ♯ n ( S 2 × S 1 ) is F n , the free group with n generators. There is a 1–1 correspondence between the equivalence classes of Z -splittings of F n and homotopy classes of imbedded essential tori in M. We define and prove a local notion of minimal intersection of a torus with respect to a maximal sphere system in M, which is inspired by Hatcherʼs work (Hatcher, 1995 [7]) on 2-spheres in the same manifold.