Homology cobordisms of 3-manifolds, knot concordances, and prime knots

Abstract

There is a close relation between link concordances and homology cobordisms of 3-manif olds. Using: this relationship we will prove that every closed, orientable 3-manif old is homology cobordant to an irreducible 3-manif old. Essentially the same construction will be used to prove that every knot in S B is concordant to a prime knot.