Abstract
In this article, we consider the compactifications of some kinds of contractible smooth affine threefolds and the characterization of the affine 3-space GIF13 keeping the 3-dimensional Zariski Cancellation Problem in mind. We classify the compactifications of contractible smooth affine threefolds with a certain condition concerning the numerical property of boundary divisors with respect to compactifications and, then, we show that if an affine threefold X satisfies X×GIF11≅GIF14 and this numerical condition, then X is isomorphic to the affine 3-space GIF13.
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