The lowest volume 3–orbifolds with high torsion

Christopher K. Atkinson, David Futer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


For each natural number n ≥ 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.

Original languageEnglish (US)
Pages (from-to)5809-5827
Number of pages19
JournalTransactions of the American Mathematical Society
Issue number8
StatePublished - 2017

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© 2017 by the authors.


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