## Affine pseudo-planes and cancellation problem

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- by Kayo Masuda and Masayoshi Miyanishi PDF
- Trans. Amer. Math. Soc.
**357**(2005), 4867-4883 Request permission

## 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.## References

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## Additional Information

**Kayo Masuda**- Affiliation: Mathematical Science II, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan
- MR Author ID: 605048
- Email: kayo@sci.himeji-tech.ac.jp
**Masayoshi Miyanishi**- Affiliation: School of Science & Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan
- Email: miyanisi@ksc.kwansei.ac.jp
- Received by editor(s): November 26, 2003
- Published electronically: July 19, 2005
- Additional Notes: This work was supported by Grant-in-Aid for Scientific Research (C), JSPS
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**357**(2005), 4867-4883 - MSC (2000): Primary 14R10; Secondary 14R20, 14R25, 14L30
- DOI: https://doi.org/10.1090/S0002-9947-05-04046-8
- MathSciNet review: 2165391