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Small covers of the dodecahedron and the $120$-cell


Authors: Anne Garrison and Richard Scott
Journal: Proc. Amer. Math. Soc. 131 (2003), 963-971
MSC (2000): Primary 57M50
DOI: https://doi.org/10.1090/S0002-9939-02-06577-2
Published electronically: June 18, 2002
MathSciNet review: 1937435
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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 homeomorphism 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

DOI: https://doi.org/10.1090/S0002-9939-02-06577-2
Keywords: Small cover, dodecahedron, $120$-cell, closed hyperbolic manifold
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
Article copyright: © Copyright 2002 American Mathematical Society

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