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

    Bibliographical note

    Funding Information:
    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.

    Publisher Copyright:
    © 2017 by the authors.

    Copyright 2017 Elsevier B.V., All rights reserved.

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