Here is as Novikov himself describes it (in russian):
Rokhlin in 1965 drew my attention repeatedly to the fact that for prime p (large enough for a given dimension), the definition of combinatorial Pontryagin-Hirzebruch classes modulo p is unknown, and this issue is not trivial. I thought about it and found an interesting "additive" property of the signature of manifolds with boundary by gluing along connected boundary components. From this we with Rokhlin extracted right definition of the classes mod p. This additive has been used by Yanih and others after the Moscow Congress, where I talked about it much, for the axiomatization of the signature. We now know that this property of the signature is equivalent in modern terminology to building an "abelian" nontrivial topological quantum field theory.
In 1965-1966 we with Rokhlin sat down to write the joint work, but could not finish it. None of us wanted to submit to another as how to write it. Work broke up, Rokhlin refused. In my preprint of the International Congress of Mathematicians in Moscow in 1966 I placed the information on this as a joint result. This preprint was published with the amendments in the collection in honor of the de Rham in 1970.
