Affine Pseudo-planes and Cancellation Problem

We define affine pseudo-planes as one class of Q-homology planes. It is shown that there exists an infinite-dimensional family of non-isomorphic affine pseudo-planes which become isomorphic to each other by taking products with the affine line A1. Moreover, we show that there exists an infinitedimensional family of the universal coverings of affine pseudo-planes with a cyclic group acting as the Galois group, which have the equivariant non-cancellation property. Our family contains the surfaces without the cancellation property, due to Danielewski-Fieseler and tom Dieck.