Cobordisms of finite quadratic forms and gluing oriented manifolds

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].…”

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

“…The needed definitions and results about lattices and forms on finite groups are given in w there we also describe gluing a unimodular lattice from two nondegenerate lattices [2,3]. A technical result on conditions for existence of a split summand in a nondegenerate lattice is presented in w In w we prove certain corollaries of the Poincar&-Lefschetz duality, which are used in the paper.…”

“…Throughout the paper, we stick to the notation and terminology used in [2,3,5]. A lattice is a free Abelian group L endowed with a symmetric bilinear integral form bL : L • L ---* Z (we often do not mention the form bL because it is assumed to be fixed).…”

“…Let M be the result of gluing these manifolds together with the help of the homeomorphism f. How can one describe the intersection form on the middle integral homology of the manifold M if the intersection forms of the manifolds M1 and M2 are known? In [2,3], we study in detail the case in which the intersection forms of the initial manifolds are nondegenerate, and the gluing is allowed even along an (open-closed) part of the boundary. In the present paper, we drop the assumption of nondegeneracy of the intersection forms of M1 and Ms.…”