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

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...

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Bibliographic Details
Published in:arXiv.org 2008-04
Main Authors: Macasieb, Melissa L, Mattman, Thomas W
Format: Article
Language:English
Subjects:
Knots
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0804.0112