  In this paper we announce a gluing theorem for conformal structures with
anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that
are more general than those considered by previous authors. By adapting a
method proposed by Floer, sufficient conditions are given for the existence of
ASD conformal structures on `generalized connected sums' of non-compact ASD
4-manifolds with cylindrical ends. The gluing theorem applies in particular to
give results about connected sums of ASD orbifolds along (isolated) singular
points.
