This is a continuation of the talk from January 13th. Gabai recently showed that the Whitehead contractible open 3-manifold is a union of two copies of R3 . After describing and exploring topological invariants of nested unions of tori, I will describe two classes of open contractible 3-manifolds. The first infinite class has the double 3-space property described by Gabai. The second infinite class fails to have this property. This is joint work with D. Wright of B.Y.U. and Dušan Repovš of the University of Ljuibljana.