Affine pseudo-planes and cancellation problem

Masuda, Kayo; Miyanishi, Masayoshi

doi:10.1090/S0002-9947-05-04046-8

Affine pseudo-planes and cancellation problem
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by Kayo Masuda and Masayoshi Miyanishi

Trans. Amer. Math. Soc. 357 (2005), 4867-4883

DOI: https://doi.org/10.1090/S0002-9947-05-04046-8

Published electronically: July 19, 2005

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Abstract:

We define affine pseudo-planes as one class of $\mathbb {Q}$-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 $\mathbb {A}^1$. Moreover, we show that there exists an infinite-dimensional 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.

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