On symplectic cobordisms

In the article, the method of spherical reconstructions of smooth manifolds is applied to the computation of some groups of symplectic cobordisms. Namely, it is proved that $\Omega^5_{Sp}=Z_2$, $\Omega^6_{Sp}=Z_2$, $\Omega^7_{Sp}=0$. The indicated values of the groups of cobordisms for dimensions 5 and 6 are known and follow from arguments of the Adams spectral sequence for $S_p$-cobordisms. The new result is the fact that the seventh group of cobordisms equals 0. This is the fundamental result of the article. The theorem concerning the reconstruction of manifolds with a quasisymplectic structure in the normal bundle, which is proved in the article, and the theorem on integer values of Atiyah–Hirzebruch constitute the basis for the proof.
Bibliography: 6 titles.