  The affine cancellation problem, which asks whether complex affine varieties
with isomorphic cylinders are themselves isomorphic, has a positive solution
for two dimensional varieties whose coordinate rings are unique factorization
domains, in particular for the affine plane, but counterexamples are found
within normal surfaces Danielewski surfaces and factorial threefolds of
logarithmic Kodaira dimension equal to 1. The latter are therefore remote from
the affine three-space, the first unknown case where the base of one cylinder
is an affine space. Locally trivial Ga-actions play a significant role in these
examples. Threefolds admitting free Ga-actions are discussed, especially a
class of varieties with negative logarithmic Kodaira dimension which are total
spaces of nonisomorphic Ga-bundles. Some members of the class are shown to be
isomorphic as abstract varieties, but it is unknown whether any members of the
class constitute counterexamples to cancellation.
