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This article is cited in 1 scientific paper (total in 1 paper)
On symplectic cobordisms
V. R. Kireitov
Abstract:
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.
Received: 15.12.1969
Citation:
V. R. Kireitov, “On symplectic cobordisms”, Mat. Sb. (N.S.), 83(125):1(9) (1970), 77–89; Math. USSR-Sb., 12:1 (1970), 77–89
Linking options:
https://www.mathnet.ru/eng/sm3502https://doi.org/10.1070/SM1970v012n01ABEH000911 https://www.mathnet.ru/eng/sm/v125/i1/p77
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Abstract page: | 256 | Russian version PDF: | 92 | English version PDF: | 8 | References: | 34 |
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