Title: Self-Gluing formula of the monopole invariant and its application,
Abstract: Given a $4$-manifold $\hat{M}$ and two homeomorphic surfaces $\Sigma_1,
\Sigma_2$ smoothly embedded in $\hat{M}$ with genus more than 1, we remove the
neighborhoods of the surfaces and obtain a new $4$-manifold $M$ from gluing two
boundaries $S^1 \times \Sigma_1$ and $S^1 \times \Sigma_1.$ In this artice, we
prove a gluing formula which describes the relation of the Seiberg-Witten
invariants of $M$ and $\hat{M}.$ 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.