Mathematical Research Letters

Volume 20 (2013)

Number 6

Small volume link orbifolds

Pages: 995 – 1016



Christopher K. Atkinson (Department of Mathematics, University of Minnesota, Morris, Mn., U.S.A.)

David Futer (Department of Mathematics, Temple University, Philadelphia, Pennsylvania, U.S.A.)


This paper proves lower bounds on the volume of a hyperbolic 3-orbifold whose singular locus is a link. We identify the unique smallest volume orbifold whose singular locus is a knot or link in the 3-sphere, or more generally in a $\mathbb{Z}_6$ homology sphere. We also prove more general lower bounds under mild homological hypotheses.

Full Text (PDF format)