Geodesic
Commensurability classes of (−2,3,n) pretzel knot complements
Macasieb, Melissa1 ; Mattman, Thomas2
1Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
2Department of Mathematics and Statistics, California State University, Chico, Chico, CA 95929-0525, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1833-1853
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Let K be a hyperbolic (−2,3,n) pretzel knot and M = S3 ∖ 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≠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.

DOI : 10.2140/agt.2008.8.1833
Keywords: commensurability class, pretzel knot, trace field

Macasieb, Melissa  1   ; Mattman, Thomas  2

1 Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
2 Department of Mathematics and Statistics, California State University, Chico, Chico, CA 95929-0525, USA 
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Macasieb, Melissa; Mattman, Thomas. Commensurability classes of (−2,3,n) pretzel knot complements. Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1833-1853. doi: 10.2140/agt.2008.8.1833

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