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Bar complex, configuration spaces and finite type invariants for braids
Authors:Toshitake Kohno
Affiliation:IPMU, Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Abstract:We show that the bar complex of the configuration space of ordered distinct points in the complex plane is acyclic. The 0-dimensional cohomology of this bar complex is identified with the space of finite type invariants for braids. We construct a universal holonomy homomorphism from the braid group to the space of horizontal chord diagrams over Q, which provides finite type invariants for braids with values in Q.
Keywords:Bar complex   Configuration space   Iterated integral   Braid group   Finite type invariants   Drinfel'd associator
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