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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the topological classification of the floors of certain Hilbert fundamental domains
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by Michael H. Hall PDF
Proc. Amer. Math. Soc. 28 (1971), 67-70 Request permission

Abstract:

Associated to the field $Q({k^{1/2}})$ ($k$ a positive square free integer greater than one), there is a group of transformations of the product of two upper half planes which is analogous to the Hilbert modular group. This group has been shown to have a fundamental domain bounded by a finite number of hypersurfaces. Of particular interest is a subspace of the domain known as the “floor.” This floor is a quotient space of a fiber bundle over the circle which is determined by the field $Q({k^{1/2}})$. The principal result of this paper is that, conversely, the topological type (indeed the homotopy type) of this fiber bundle determines the field $Q({k^{1/2}})$ which gives rise to it. This is accomplished by computing the homology groups of the fiber space and showing that the integer $k$ can be determined from these groups.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 67-70
  • MSC: Primary 10.21
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0271029-3
  • MathSciNet review: 0271029