Guts and volume for hyperbolic $3$-orbifolds with underlying space $S^3$

Abstract

For a hyperbolic 3-orbifold with underlying space the 3-sphere, we obtain a lower bound on its volume in the case that it contains an essential 2-suborbifold with underlying space the 2-sphere with four cone points. Our techniques involve computing the guts of the orbifold split along the 2suborbifold via a careful analysis of its topology. We also characterize the orbifolds of this type that have empty guts.