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SUMMARY:Set theory and algebraic topology - Brooke-Taylor\, A (University 
 of Bristol)
DTSTART:20151218T133000Z
DTEND:20151218T143000Z
UID:TALK62973@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:In this talk I plan to discuss some joint work with Sheila Mil
 ler related to knots.  Quandles are algebraic structures that can be assoc
 iated to (tame) knots\, and they in fact constitute one of the few complet
 e invariants we have for knots.  However\, there is some dissatisfaction w
 ith quandles as invariants\, as it heuristically seems difficult to determ
 ine whether two quandles are isomorphic.  Our result supports this impress
 ion: 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 reduci
 bility perspective\, raising the prospect that more manageable complete in
 variants might exist.\n
LOCATION:Seminar Room 1\, Newton Institute
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