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Transactions of the American Mathematical Society

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The lowest volume $ 3$-orbifolds with high torsion


Authors: Christopher K. Atkinson and David Futer
Journal: Trans. Amer. Math. Soc. 369 (2017), 5809-5827
MSC (2010): Primary 57M50, 57M60, 57R18
DOI: https://doi.org/10.1090/tran/6920
Published electronically: April 13, 2017
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Abstract: For each natural number $ n \geq 4$, we determine the unique lowest volume hyperbolic $ 3$-orbifold whose torsion orders are bounded below by $ n$. This lowest volume orbifold has base space the $ 3$-sphere and singular locus the figure-$ 8$ knot, marked $ n$. We apply this result to give sharp lower bounds on the volume of a hyperbolic manifold in terms of the order of elements in its symmetry group.


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Additional Information

Christopher K. Atkinson
Affiliation: Division of Science and Mathematics, University of Minnesota Morris, Morris, Minnesota 56267
Email: catkinso@morris.umn.edu

David Futer
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: dfuter@temple.edu

DOI: https://doi.org/10.1090/tran/6920
Received by editor(s): August 19, 2015
Received by editor(s) in revised form: February 15, 2016
Published electronically: April 13, 2017
Additional Notes: The second author was supported in part by NSF grant DMS–1408682 and the Elinor Lunder Founders’ Circle Membership at the Institute for Advanced Study.
Article copyright: © Copyright 2017 by the authors

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