On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the twist knots

Abstract

For a twist knot ${\mathcal{K}}_{p^{\prime }}$, let $M$ be the closed $3$-manifold obtained by doing $(p,q)$ Dehn-filling along ${\mathcal{K}}_{p^{\prime }}$. In this article, we prove that Chen-Yang's volume conjecture holds for sufficiently large $|p|+|q|$ and $|p^{\prime }|$ for $M$. In the proof, we construct a new ideal triangulation of the Whitehead link complement which is different from Thurston's triangulation. Our triangulation has led to some new discoveries regarding symmetry, including insights into ``sister manifolds'' as introduced by Hodgson, Meyerhoff, and Weeks.

58 pages, 34 figures