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Commensurability classes of 2-bridge knot complements. (English) Zbl 1154.57001
The authors show that a hyperbolic 2-bridge knot complement is the unique knot complement in its commensurability class. They also discuss constructions of commensurable knot complements and conjecture that, for any hyperbolic knot \(K\), there are at most three knot complements in the commensurability class of \(S^3 \setminus K\). Furthermore, they conjecture that if \(K\) additionally has no symmetries or hidden symmetries, then \(S^3 \setminus K\) is the unique knot complement in its commensurability class.

MSC:
57M10 Covering spaces and low-dimensional topology
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
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