Set theory and algebraic topology
Duration: 57 mins 56 secs
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About this item
| Description: |
Brooke-Taylor, A (University of Bristol)
Friday 18th December 2015 - 13:30 to 14:30 |
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| Created: | 2015-12-23 14:57 |
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| Collection: | Mathematical, Foundational and Computational Aspects of the Higher Infinite |
| Publisher: | Isaac Newton Institute |
| Copyright: | Brooke-Taylor, A |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | 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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