Cobordisms of manifolds with boundary

We shall outline the theory of cobordisms of manifolds with boundary, starting from a suitably defined Morse function. As an application we shall show new results in the theory of higher dimensional links: each closed oriented manifolds M^{2n-1} in S^{2n+1} admits a Seifert surface and different Seifert surfaces give rise to S-equivalent Seifert matrices. This result has application in the theory of deformations of hypersurface singularities. This is a joint project with A. Nemethi and A. Ranicki.