Flat connections on configuration spaces and formality of braid groups of surfaces

Abstract

We construct an explicit bundle with flat connection on the configuration space of n points of a complex curve. This enables one to recover the `formality' isomorphism between the Lie algebra of the prounipotent completion of the pure braid group of n points on a surface and an explicitly presented Lie algebra t_{g,n} (Bezrukavnikov), and to extend it to a morphism from the full braid group of the surface to the semidirect product exp(hat t_{g,n}) rtimes S_n.

18 pages

References in corpus (1)

• Towards multiple elliptic polylogarithms

Cited by in corpus (6)

• Cyclotomic associators and finite type invariants for tangles in the solid torus
• On the universal ellipsitomic KZB connection
• Universal KZB Equations for arbitrary root systems
• Surface Drinfeld Torsors I : Higher Genus Associators
• 1-minimal models for $C_{\infty }$-algebras and flat connections
• A construction of single-valued elliptic polylogarithms