Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition

Colin Adams, Michele Capovilla-Searle, Darin Li, Lily Qiao Li, Jacob McErlean, Alexander Simons, Natalie Stewart, Xiwen Wang

Published 2021-11-11Version 1

In a variety of settings we provide a method for decomposing a 3-manifold $M$ into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold $M$ is hyperbolic and its volume is bounded below by the sum of the appropriately defined hyperbolic volumes of the pieces. A variety of examples of appropriately hyperbolic pieces and volumes are provided, with many examples from link complements in the 3-sphere.