Hi!

Novikov's additivity theorem states that if you glue together two compact oriented 4n-manifolds along a connected component of their boundaries, the signature of the resulting manifold is simply the sum of the signatures of the pieces. It is proved for example in Kirby's *The Topology of 4-manifolds* and Kauffman's *On Knots*.

However, I haven't found any direct reference to an original article of Novikov's on this topic. Sometimes, *The index of elliptic operators III* by Atiyah and Singer is given as a reference.

So my questions are : what is the original reference? Has Novikov written this result in any of his papers? What has happened between Novikov's first proof and the one by Atiyah and Singer?

Any comment on this topic will be appreciated.