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We consider two well known constructions of link invariants. One uses skeintheory: you resolve each crossing of the link as a linear combination of thingsthat don't cross, until you eventually get a linear combination of links withno crossings, which you turn into a polynomial. The other uses quantum groups:you construct a functor from a topological category to some category ofrepresentations in such a way that (directed framed) links get sent toendomorphisms of the trivial representation, which are just rational functions.Certain instances of these two constructions give rise to essentially the sameinvariants, but when one carefully matches them there is a minus sign thatseems out of place. We discuss exactly how the constructions match up in thecase of the Jones polynomial, and where the minus sign comes from. On thequantum group side, one is led to use a non-standard ribbon element, which thenallows one to consider a larger topological category.

A minus sign that used to annoy me but now I know why it is there