2016/02/09 by Brooke-Taylor, Andrew D., Miller, Sheila K.
#03E15 #20N99 #57M27 #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1602.03209
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.