一个纽结不变量的Borel完备性
The quandary of quandles: The Borel completeness of a knot invariant
摘要：
Joyce引入的纽结quandle的同构类型是Tame纽结的完全不变量。两个quandles是否同构是在实践中很难确定，我们证明，这个问题是可证明的困难：同构的quandles是博雷尔完成。然而，从博雷尔约化的角度来看，驯服的节类是微不足道的，这表明驯服的节的等价性可以被约化为一个更容易处理的同构问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
