Abstract
We develop certain discriminant form techniques allowing one to “glue” two integral lattices into a new lattice. In particular, we introduce the notion of fusion of finite forms, which is closely connected with the more familiar notion of cobordism of such forms. We also consider the category of finite forms and their cobordisms. These techniques are used for describing the intersection form of a compact oriented 4k-manifold M obtained by gluing together two manifolds M1 and M2 along one or several boundary components (the intersection forms of M1 and M2 are assumed to be nondegenerate). Bibliography: 12 titles.
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