Logic Seminar-The isomorphism problem for quandles is complicated

Time: Wednesday, September 6, 11:15am – 12:15pm

Place: Monroe Hall, Room 250

Speaker:  Henry Klatt, GWU

Title: The isomorphism problem for quandles is complicated

Abstract:  Quandles are algebraic structures that were introduced by David Joyce in his 1982 PhD thesis. The axiomatization is in some sense an algebratization of the Reidemeister moves of knot theory, which leads naturally to the definition of the so-called fundamental quandle of a knot. The fundamental quandle is, in fact, a complete invariant; i.e., two knots are equivalent under ambient isotopy if and only if they have isomorphic fundamental quandles. However, in general, the quandle isomorphism problem is quite complicated. From the point of view of descriptive set theory, the problem is in some sense maximally complicated. In this talk, we will demonstrate the Borel completeness of the quandle isomorphism problem when coded as a relation on the Cantor space.