Bar complex, configuration spaces and finite type invariants for braids |
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Authors: | Toshitake Kohno |
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Affiliation: | IPMU, Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan |
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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. |
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Keywords: | Bar complex Configuration space Iterated integral Braid group Finite type invariants Drinfel'd associator |
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