Cobordism of surfaces embedded in S4

We show that a closed connected Surface embedded in S-4 = partial derivative B-5 bounds a handlebody of dimension 3 embedded in B-5 if and only if the Euler number of its normal bundle vanishes. Using this characterization, we show that two closed connected surfaces embedded in S-4 are cobordant if and only if they are abstractly diffeomorphic to each other and the Euler numbers of their normal bundles coincide. As an application, we show that a given Heegaard decomposition of a 3-manifold can be realized in S-5. We also give a new proof of Rohlin's theorem on ernbeddings of 3-manifolds into R-5.