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

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. Bibl. 6 titles.