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Set theory and algebraic topology

Presented by: 
A Brooke-Taylor University of Bristol
Friday 18th December 2015 - 13:30 to 14:30
INI Seminar Room 1
In this talk I plan to discuss some joint work with Sheila Miller related to knots. Quandles are algebraic structures that can be associated to (tame) knots, and they in fact constitute one of the few complete invariants we have for knots. However, there is some dissatisfaction with quandles as invariants, as it heuristically seems difficult to determine whether two quandles are isomorphic. Our result supports this impression: we show that the isomorphism relation of quandles is as complex as it possibly could be in Borel reducibility terms, being Borel complete. On the other hand, equivalence of tame knots is trivial from a Borel reducibility perspective, raising the prospect that more manageable complete invariants might exist.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons