Faculty Publications
Publication Date
2016
Disciplines
Geometry and Topology | Mathematics
Abstract
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.
Document Type
Published Version
Rights
First published by Mathematical Sciences Publishers in Pacific Journal of Mathematics, 285(2), 2016.
Original Citation
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
doi:10.2140/pjm.2016.285.453
DigitalCommons@Linfield Citation
Millichap, Christian and Worden, William, "Hidden Symmetries and Commensurability of 2-Bridge Link Complements" (2016). Faculty Publications. Published Version. Submission 9.
https://digitalcommons.linfield.edu/mathfac_pubs/9
Comments
This article is the publisher-created version, also considered to be the final version or the version of record. It includes value-added elements provided by the publisher, such as copy editing, layout changes, and branding consistent with the rest of the publication.