Attaching handles to delaunay nodoids

For all m ∈ N-{0}, we prove the existence of a one-dimensional family of genus m, constant mean curvature (equal to 1) surfaces which are complete, immersed in R3, and have two Delaunay ends asymptotic to nodoidal ends. Moreover, these surfaces are invariant under the group of isometries of R³ leaving a horizontal regular polygon with mC1 sides fixed.