Geodesic
Realization of quadratic forms by smooth manifolds
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 177-184

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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. 
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     author = {I. O. Kalinin},
     title = {Realization of quadratic forms by smooth manifolds},
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I. O. Kalinin. Realization of quadratic forms by smooth manifolds. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 177-184. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a11/