Geometry and Topology | Mathematics
In this paper, we show that any nonarithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of 3-manifolds with nontrivial JSJ-decomposition and rank-two fundamental groups. We also show that the only commensurable hyperbolic 2-bridge link complements are the figure-eight knot complement and the 622 link complement. Our work requires a careful analysis of the tilings of R2 that come from lifting the canonical triangulations of the cusps of hyperbolic 2-bridge link complements.
First published by Mathematical Sciences Publishers in Pacific Journal of Mathematics, 285(2), 2016.
Christian Millichap & William Worden
Hidden symmetries and commensurability of 2-bridge link complements.
Pacific Journal of Mathematics, 2016, volume 285, issue 2, pages 453-484
Millichap, Christian and Worden, William, "Hidden Symmetries and Commensurability of 2-Bridge Link Complements" (2016). Faculty Publications. Published Version. Submission 9.