Small volume link orbifolds

TL;DR

This paper establishes lower bounds on the volume of hyperbolic 3-orbifolds with link singular loci, identifying the smallest such orbifolds in specific homological contexts and providing general bounds under mild conditions.

Contribution

It introduces new lower bounds for volumes of hyperbolic 3-orbifolds with link singularities and identifies the unique minimal volume orbifolds in certain homological settings.

Findings

Identified the smallest volume hyperbolic 3-orbifold with a knot or link singularity.

Proved lower bounds on volume for orbifolds with specified homological properties.

Characterized the minimal volume orbifolds in the context of Z_6 homology spheres.

Abstract

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 Z_6 homology sphere. We also prove more general lower bounds under mild homological hypotheses.