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arXiv · 1602.03209

The quandary of quandles: The Borel completeness of a knot invariant

Andrew D. Brooke-Taylor·Sheila K. Miller
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Abstract

The isomorphism type of the knot quandle introduced by Joyce is a complete invariant of tame knots. Whether two quandles are isomorphic is in practice difficult to determine; we show that this question is provably hard: isomorphism of quandles is Borel complete. The class of tame knots, however, is trivial from the perspective of Borel reducibility, suggesting that equivalence of tame knots may be reducible to a more tractable isomorphism problem.

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Andrew D. Brooke-Taylor, Sheila K. Miller. 2016-02-09. The quandary of quandles: The Borel completeness of a knot invariant. https://arxiv.org/abs/1602.03209

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