  For smooth embeddings of an integral homology 3-sphere in the 6-sphere, we
define an integer invariant in terms of their Seifert surfaces. Our invariant
gives a bijection between the set of smooth isotopy classes of such embeddings
and the integers. It also gives rise to a complete invariant for homology
bordism classes of all embeddings of homology 3-spheres in the 6-sphere. As a
consequence, we show that two embeddings of an oriented integral homology
3-sphere in the 6-sphere are isotopic if and only if they are homology bordant.
We also relate our invariant to the Rohlin invariant and accordingly
characterise those embeddings which are compressible into the 5-sphere.

Geometric Topology;Algebraic Topology