The lowest volume 3-orbifolds with high torsion

Christopher K. Atkinson; David Futer

doi:10.1090/tran/6920

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arXiv · 1507.07894

The lowest volume 3-orbifolds with high torsion

Christopher K. Atkinson·David Futer

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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.

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BibTeX RIS

Christopher K. Atkinson, David Futer. 2016-02-18. The lowest volume 3-orbifolds with high torsion. https://doi.org/10.1090/tran%2F6920

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