Self-Gluing formula of the monopole invariant and its application

Original · EN

Given a 4-manifold M and two homeomorphic surfaces Σ₁, Σ₂ smoothly embedded in M with genus more than 1, we remove the neighborhoods of the surfaces and obtain a new 4-manifold M from gluing two boundaries S¹ × Σ₁ and S¹ × Σ₁. In this artice, we prove a gluing formula which describes the relation of the Seiberg-Witten invariants of M and M. Moreover, we show the application of the formula on the existence condition of the symplectic structure on a family of 4-manfolds under some conditions.