Flat connections on configuration spaces and formality of braid groups of surfaces
Geometric Topology
2011-12-06 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1112.0864,
title = {Flat connections on configuration spaces and formality of braid groups of surfaces},
author = {B. Enriquez},
journal= {arXiv preprint arXiv:1112.0864},
year = {2011}
}
Comments
18 pages