  We give a simple axiomatic definition of a rational-valued invariant s(W,V,e)
of triples (W,V,e), where W is a (smooth, oriented, closed) 6-manifold and V is
a 3-submanifold of W, and where e is a second rational cohomology class of the
complement of V satisfying a certain condition. The definition is stated in
terms of cobordisms of such triples and the signature of 4-manifolds. When W =
S^6 and V is a smoothly embedded 3-sphere, and when e/2 is the Poincare dual of
a Seifert surface of V, the invariant coincides with -8 times Haefliger's
embedding invariant of (S^6,V). Our definition recovers a more general
invariant due to Takase, and contains a new definition for Milnor's triple
linking number of algebraically split 3-component links in R^3 that is close to
the one given by the perturbative series expansion of the Chern-Simons theory
of links in R^3.
