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So, there's a construction of Reshetikhin and Turaev which extracts knot invariants from ribbon monoidal categories, which are (usually) the representation category a Hopf algebra with a choice of ribbon element. How do these knot invariants change if I pick a different ribbon element in the same Hopf algebra? In particular, will something strange happen with 3-manifold invariants? |
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How do quantum knot invariants change when I pick a funny ribbon element?So, there's a construction of Reshetikhin and Turaev which extracts knot invariants from ribbon monoidal categories, which are (usually) the representation category a Hopf algebra with a choice of ribbon element. How do these knot invariants change if I pick a different ribbon element in the same Hopf algebra?
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