#### Volume 8, issue 3 (2008)

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

### Melissa L Macasieb and Thomas W Mattman

Algebraic & Geometric Topology 8 (2008) 1833–1853
##### Abstract

Let $K$ be a hyperbolic $\left(-2,3,n\right)$ pretzel knot and $M={S}^{3}\setminus K$ 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 $n\ne 7$, 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.

##### Keywords
commensurability class, pretzel knot, trace field
Primary: 57M25