Realizing pairs of multicurves as cylinders on translation surfaces

Any pair of intersecting cylinders on a translation surface is "coherent," in that the geometric and algebraic intersection numbers of their core curves are equal (up to sign).In this paper, we investigate when a pair of multicurves can be simultaneously realized as the core curves of cylinders on some translation surface.Our main tools are surface topology and the "flat grafting" deformation introduced by Ser-Wei Fu.