Geodesic
On symplectic cobordisms
Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 77-89 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On~symplectic cobordisms},
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}
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V. R. Kireitov. On symplectic cobordisms. Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 77-89. http://geodesic.mathdoc.fr/item/SM_1970_12_1_a4/

[1] R. Bott, “$K$-teoriya”, Matematika, 11:2 (1967), 32–56 | MR

[2] R. Bott, “The stable homotopy of the classical groups”, Ann. Math., 70 (1959), 313–337 | DOI | MR | Zbl

[3] Dzh. Milnor, “Lektsiya o kharakteristicheskikh klassakh”, Matematika, 1965, no. 4, 3–40

[4] J. Milnor, “Remarks concerning Spin manifolds”, Differential and combinatorial topology, Princeton University Press, Princeton–New Jersey, 1965 | MR

[5] S. P. Novikov, “Gomotopicheskie ekvivalentnye gladkie mnogoobraziya”, Izv. AN SSSR, seriya matem., 28:2 (1964), 365–474 | MR

[6] F. Khirtsebrukh, “Kompleksnye mnogoobraziya”, Mezhdunarodnyi matematicheskii kongress v Edinburge, Fizmatgiz, Moskva, 1962