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

Christopher K. Atkinson; Jessica Mallepalle; Joseph Melby; Shawn Rafalski; Jennifer Vaccaro

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arXiv · 1703.04160

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

Christopher K. Atkinson·Jessica Mallepalle·Joseph Melby·Shawn Rafalski·Jennifer Vaccaro

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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 $2$-suborbifold via a careful analysis of its topology. We also characterize the orbifolds of this type that have empty guts.

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Christopher K. Atkinson, Jessica Mallepalle, Joseph Melby, Shawn Rafalski, Jennifer Vaccaro. 2017-03-12. Guts and volume for hyperbolic $3$-orbifolds with underlying space $S^3$. https://arxiv.org/abs/1703.04160

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