The lowest volume 3–orbifolds with high torsion

Christopher K. Atkinson; David Futer

doi:10.1090/tran/6920

The lowest volume 3–orbifolds with high torsion

Christopher K. Atkinson, David Futer

Research output: Contribution to journal › Article › peer-review

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Abstract

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 language	English (US)
Pages (from-to)	5809-5827
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	369
Issue number	8
DOIs	https://doi.org/10.1090/tran/6920
State	Published - 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.

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The lowest volume 3–orbifolds with high torsion

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