Hidden Symmetries and Commensurability of 2-Bridge Link Complements
| Autor: | Christian Millichap, William Worden |
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| Rok vydání: | 2016 |
| Předmět: |
Knot complement
Pure mathematics General Mathematics 010102 general mathematics Geometric Topology (math.GT) 01 natural sciences Commensurability (mathematics) Mathematics::Geometric Topology 57M50 Mathematics - Geometric Topology Corollary 0103 physical sciences Homogeneous space FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1601.01015 |
| Popis: | In this paper, we show that any non-arithmetic 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 non-trivial 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 $6_{2}^{2}$ link complement. Our work requires a careful analysis of the tilings of $\mathbb{R}^{2}$ that come from lifting the canonical triangulations of the cusps of hyperbolic $2$-bridge link complements. Comment: This is the final (accepted) version of this paper |
| Databáze: | OpenAIRE |
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