Realization of quadratic forms by smooth manifolds

It is proved in this paper that, for every $k>1$, each integral unimodular quadratic form is the intersection index form of some smooth closed manifold of dimension $4k$. The question is also studied of the realizability of such forms by manifolds with additional structures on the stable normal bundle and, as a consequence, of the realizability of forms by highly connected manifolds.
Bibliography: 10 titles.