Connecting Homomorphism and Separating Cycles

We discuss the construction of a long semi-exact Mayer–Vietoris sequence for homology any finite union open subspaces. This is used to obtain topological conditions representation integral meromorphic n-form on an n-dimensional complex manifold in terms Grothendieck residues. For such exist, it necessary that cycle integration separates set polar hypersurfaces form. The separation condition number cases turns out be sufficient representing as sum Earlier, when describing (in works Tsikh, Yuzhakov, Ulvert, etc.), key was Stein. main result this article relaxation