Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition

TL;DR

This paper introduces a decomposition method for 3-manifolds into hyperbolic pieces, establishing lower bounds on their volumes, with applications to link complements in the 3-sphere.

Contribution

It provides a novel approach to estimate hyperbolic volumes of 3-manifolds through decomposition into hyperbolic components, expanding tools for volume bounds.

Findings

Decomposition method yields volume lower bounds for hyperbolic 3-manifolds.

Examples include link complements in the 3-sphere demonstrating the method.

The approach applies to various hyperbolic pieces, broadening volume estimation techniques.

Abstract

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.