English

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}
}

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18 pages