The lowest volume 3-orbifolds with high torsion
arXiv:1507.07894 · doi:10.1090/tran/6920
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.
17 pages, 1 figure. v2 contains minor edits. To appear in Transactions of the AMS