Abstract
Let X be a Riemann surface of positive genus. Denote by X(n) the configuration space of n distinct points on X. We use the Betti–de Rham comparison isomorphism on H1(X(n)) to define an integrable connection on the trivial vector bundle on X(n) with fiber the universal algebra of the Lie algebra associated with the descending central series of π1 of X(n). The construction is inspired by the Knizhnik–Zamolodchikov system in genus zero and its integrability follows from Riemann period relations.
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