Splittings of manifolds with boundary and related invariants

We construct special handle decompositions for a compact connected PL manifold with non empty boundary and study the associated topological invariants. As a consequence, we characterize the unknot in the (n+2)-sphere (n less or equal 2) as the unique n-knot whose complement has genus one. Then we obtain a simple geometric proof of the non cancellation theorem for tame n-knots in the (n+2)-sphere, for n less or equal 2.