Flat connections on configuration spaces and braid groups of surfaces |
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Authors: | Benjamin Enriquez |
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Institution: | IRMA (CNRS), Université de Strasbourg, 7 rue René Descartes, F-67084 Strasbourg, France |
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Abstract: | We construct an explicit bundle with flat connection on the configuration space of n points on a complex curve. This enables one to recover the ‘1-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, and to extend it to a morphism from the full braid group of the surface to the semidirect product of the associated group with the symmetric group Sn. |
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Keywords: | Braid groups of surfaces 1-Formality isomorphisms Prounipotent completions Flat connections Knizhnik&ndash Zamolodchikov&ndash Bernard connections |
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