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

Melissa L. Macasieb; Thomas W. Mattman

doi:10.2140/agt.2008.8.1833

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arXiv · 0804.0112

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

Melissa L. Macasieb·Thomas W. Mattman

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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.

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BibTeX RIS

Melissa L. Macasieb, Thomas W. Mattman. 2008-04-01. Commensurability classes of (-2,3,n) pretzel knot complements. https://doi.org/10.2140/agt.2008.8.1833

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