Commensurability classes of (-2,3,n) pretzel knot complements

Abstract

Let K be a hyperbolic (-2,3,n) pretzel knot and M = S^3 K its complement. For these knots, we verify a conjecture of Reid and Walsh: there are at most three knot complements in the commensurability class of M. Indeed, if n \neq 7, we show that M is the unique knot complement in its class. We include examples to illustrate how our methods apply to a broad class of Montesinos knots.

15 pages, 1 figure

References in corpus (1)

• Commensurability classes of 2-bridge knot complements

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• Commensurability classes containing three knot complements
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