Trace-field symmetry conjecture for (2,3,n)(-2,3,n) pretzel knots

Let nn be an odd, negative integer, and let the trace field of a hyperbolic knot complement mean its invariant trace field. Trace-field symmetry conjecture. The (2,3,n)(-2,3,n) and (2,3,6n)(-2,3,6-n) pretzel knots have the same trace field. This symmetry would reduce the study of the trace fields to negative odd nn; the source presents it as a conjecture and uses it to motivate the subsequent arguments, while the supplied text does not establish its resolution.

Sources & referencesView supporting material

Primary source

Melissa L. Macasieb and Thomas W. Mattman, “Commensurability classes of (-2,3,n) pretzel knot complements”, arXiv:0804.0112 (2008).

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