On Steenrod's realization of cycles problem. There is old problem of realization homology classes of (closed) manifold $M^n$ by fundamental classes of its submanifolds. Partially it was solved by René Thom in his "Quelques propriétés globales des variétés différentiables", according to his results, every homology class $z_k$ with $k<6$ is realizable by some submanifold. It seems to be well known, that this result is also true for $k=6$. Is there some articles, where one could find such a proof?
P.S. I'm sorry for repeating this question again, but I did not find any proper answers there or anywhere...

Rudyak's article The problem of realization of homology classes from Poincare up to the present seems to be a good starting point.
The original paper is Thom's Quelques propriétés globales des variétés différentiables.
