Generalized knot complements and some aspherical ribbon disc complements

We generalize some aspects of standard knot-theory to all ribbon-disc complements. We study asphericity of the complement of properly embedded links in certain contractible singular 3-manifolds that should be thought off as replacements of the 3-ball in the classical setting. We apply our results to show asphericity of 2-complexes modelled on labelled oriented graphs that correspond to alternating prime projections on some surface.