HOLONOMIES FOR CONNECTIONS WITH VALUES IN L∞-ALGEBRAS.

Given a at connection α on a manifoldM with values in a filtered L∞-algebra g, we construct a morphism holα∞ : C·(M) → BU∞(g), which generalizes the holonomy map associated to a at connection with values in a Lie algebra. The construction is based on Gugenheim's A∞-version of de Rham's theorem, which in turn is based on Chen's iterated integrals. Finally, we discuss examples related to the geometry of configuration spaces of points in Euclidean space Rd, and to generalizations of the holonomy representations of braid groups. [ABSTRACT FROM AUTHOR]