## The lowest volume $3$–orbifolds with high torsion

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- by Christopher K. Atkinson and David Futer PDF
- Trans. Amer. Math. Soc.
**369**(2017), 5809-5827

## 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.## References

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## Additional Information

**Christopher K. Atkinson**- Affiliation: Division of Science and Mathematics, University of Minnesota Morris, Morris, Minnesota 56267
- MR Author ID: 873749
- Email: catkinso@morris.umn.edu
**David Futer**- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- MR Author ID: 671567
- ORCID: 0000-0002-2595-6274
- Email: dfuter@temple.edu
- 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.
- © Copyright 2017 by the authors
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 5809-5827 - MSC (2010): Primary 57M50, 57M60, 57R18
- DOI: https://doi.org/10.1090/tran/6920
- MathSciNet review: 3646779