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Affine pseudo-planes and cancellation problem


Authors: Kayo Masuda and Masayoshi Miyanishi
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
Published electronically: July 19, 2005
MathSciNet review: 2165391
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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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Additional Information

Kayo Masuda
Affiliation: Mathematical Science II, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan
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

DOI: https://doi.org/10.1090/S0002-9947-05-04046-8
Keywords: Equivariant Cancellation Problem, algebraic group action
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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