Title: Small volume link orbifolds
Abstract: I will discuss recent investigations of small volume hyperbolic 3-orbifolds whose singular locus is a link. An orbifold of this type naturally arises as the quotient of a 3-manifold under a (nice) group action. Thus, lower bounds on the volume of these orbifolds lead to relations between the volume of a 3-manifold and the size of its symmetry group.
In the special case where the singular locus is a knot in the 3-sphere, we identify the smallest volume example. We will also describe more general results on lower volume bounds for hyperbolic 3-orbifolds with singular locus a link and identify the smallest volume example in certain cases. Joint work with Chris Atkinson.