Connected sum construction of constant Q-curvature manifolds in higher dimensions

For a compact Riemannian manifold (M,g2)(M,g2) with constant Q  -curvature of dimension n≥6n≥6 satisfying nondegeneracy condition, we show that one can construct many examples of constant Q  -curvature manifolds by gluing construction. We provide a general procedure of gluing together (M,g2)(M,g2) with any compact manifold (N,g1)(N,g1) satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant Q-curvature on the connected sum N#M.