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The intersection form of the result of gluing manifolds with degenerate intersection forms

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Abstract

It is proved that the intersection form of the result of gluing together two compact oriented 4k-dimensional manifolds along their boundaries can be (noncanonically) represented as the direct sum of a split form, whose rank is determined by the images of the inclusions of the free parts of the middle homology groups of the boundaries, and a form which is the result of gluing together nondegenerate parts of the intersection forms of the initial manifolds. Bibliography: 6 titles.

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References

  1. O. A. Ivanov and N. Yu. Netsvetaev, “On the behavior of the intersection forms when gluing manifolds,” in:Abstracts of the 3rd All-Union School “The Pontryagin Readings”, Kemerovo (1990), p. 27.

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  3. O. A. Ivanov and N. Yu. Netsvetaev, “Cobordisms of finite quadratic forms and gluing oriented manifolds,”Zap. Nauchn. Semin. POMI,208, 115–132 (1993).

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Authors
  1. O. A. Ivanov
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  2. N. Yu. Netsvetaev
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 169–179.

Translated by O. A. Ivanov and N. Yu. Netsvetaev.

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Ivanov, O.A., Netsvetaev, N.Y. The intersection form of the result of gluing manifolds with degenerate intersection forms. J Math Sci 91, 3440–3447 (1998). https://doi.org/10.1007/BF02434920

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  • DOI: https://doi.org/10.1007/BF02434920

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