Deformations and gluing of asymptotically cylindrical associatives
Given a matching pair of asymptotically cylindrical (Acyl) G2 manifolds the twisted connected sum construction produces a one parameter family of closed G2 manifolds. We describe when we can construct closed rigid associatives in these closed G2 manifolds by gluing suitable pairs of Acyl associatives in the matching pair of Acyl G2 manifolds. The hypothesis and analysis in the gluing theorem requires some understanding of the deformation theory of Acyl associatives which will also be discussed. At the end we will describe examples of closed associatives coming from Acyl holomorphic curves or special Lagrangians.