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

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 ks the result of gluing together nondegenerate parts of the intersection forms of the initial manifolds. Bibliography: 6 titles.

On deformations of singular plane sextics

“…The anti-isometry κ as above is the homomorphism induced by the identification of the boundaries (which is orientation-reversing). For more details, see, e.g., O. Ivanov and N. Netsvetaev [IN1] and [IN2].…”