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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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