  We study the concordance and bordism of decompositions associated with
defining sequences and we relate them to some invariants of toroidal
decompositions and to the cobordism of homology manifolds. These decompositions
are often wild Cantor sets and they arise as nested intersections of knotted
solid tori. We show that there are at least uncountably many concordance
classes of such decompositions in the 3-sphere.
