Knizhnik-zamolodchikov Bundles Are Topologically Trivial

We prove that the vector bundles at the core of the KnizhnikZamolodchikov and quantum constructions of braid groups representations are topologically trivial bundles. We provide partial generalizations of this result to generalized braid groups. A crucial intermediate result is that the representation ring of the symmetric group on n letters is generated by the alternating powers of its natural n-dimensional representation.