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Hidden Symmetries And Commensurability Of 2-Bridge Link Complements, Christian Millichap, William Worden

Faculty Publications

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 …