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

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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 (−2,3,6−n)(-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.

References

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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