Reducible connections in massless topological QCD and 4-manifolds Original Research Article

The role of reducible connections in non-Abelian Seiberg-Witten invariants is analyzed with massless topological QCD where the monopole is extended to the non-Abelian group version. By giving small external fields, we found that the vacuum expectation value can be separated into a part from Donaldson theory, a part from Abelian monopole theory and a part from non-Abelian monopole theory. As a by-product, we find identities of U(1) topological invariants. In our proof, the duality relation and the Higgs mechanism are not necessary.