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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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Small covers of the dodecahedron and the $120$-cell
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by Anne Garrison and Richard Scott PDF
Proc. Amer. Math. Soc. 131 (2003), 963-971 Request permission

Abstract:

Let $P$ be the right-angled hyperbolic dodecahedron or $120$-cell, and let $W$ be the group generated by reflections across codimension-one faces of $P$. We prove that if $\Gamma \subset W$ is a torsion free subgroup of minimal index, then the corresponding hyperbolic manifold ${\mathbb H}^n/\Gamma$ is determined up to home omorphism by $\Gamma$ modulo symmetries of $P$.
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Additional Information
  • Anne Garrison
  • Affiliation: Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, California 95053
  • Email: agarriso@math.scu.edu
  • Richard Scott
  • Affiliation: Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, California 95053
  • Email: rscott@math.scu.edu
  • Received by editor(s): July 19, 2001
  • Received by editor(s) in revised form: October 22, 2001
  • Published electronically: June 18, 2002
  • Additional Notes: The second author was supported by an Arthur Vining Davis Fellowship from Santa Clara University
  • Communicated by: Ronald A. Fintushel
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 963-971
  • MSC (2000): Primary 57M50
  • DOI: https://doi.org/10.1090/S0002-9939-02-06577-2
  • MathSciNet review: 1937435