Abstract
Let (M 1,M 2,N) be three symplectic manifolds and suppose that we can do the symplectic connected sum of M 1 and M 2 along their submanifold N to obtain M 1#N M 2. In this paper, we consider the bilinear and cubic forms of H*(M 1#N M 2, ℤ) when dimM 1#N M 2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M 1#N M 2 and M 1∐M 2.
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Jupp, P. E.: Classification of certain 6-manifolds. Proc. Cambridge Philos. Soc., 73, 293–300 (1973)
Okonek, Ch., Van de Ven, A.: Cubic forms and complex 3-folds. Enseign. Math.(2), 41(3–4), 297–333 (1995)
Wall, C. T. C.: Classification problems in differential topology. V. On certain 6-manifolds. Invent. Math., 1, 355–374 (1966); corrigendum, ibid 2 1966 306
Zhubr, A. V.: Classification of simply connected, six-dimensional manifolds (in Russian). Dokl. Akad. Nauk SSSR, 255(6), 1312–1315 (1980)
McDuff, D.: Examples of simply-connected symplectic non-Kählerian manifold. J. Differential Geometry, 20, 267–277 (1984)
Thurston, W. P.: Some simple examples of symplectic manifolds. Proc. Amer. Math. Soc., 55(2), 467–468 (1976)
Gompf, R. E.: A new construction of symplectic manifolds. Ann. of Math. (2), 142(3), 527–595 (1995)
Halic, M.: On the geography of symplectic 6-manifolds. Manuscripta Math., 99(3), 371–381 (1999)
Gompf, R. E., Stipsicz, A. I.: 4-manifolds and Kirby calculus. Graduate Studies in Mathematics, 20, American Mathematical Society, Providence, RI, 1999, xvi+558 pp.
Hatcher, A.: Algebraic Topology, Cambridge University Press, Cambridge, 2002, xii+544 pp.
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Wang, W. On the bilinear and cubic forms of some symplectic connected sums. Acta. Math. Sin.-English Ser. 28, 1809–1822 (2012). https://doi.org/10.1007/s10114-012-0574-5
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DOI: https://doi.org/10.1007/s10114-012-0574-5