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The total homology of the loop space of the configuration space of ordered distinct n points in Rm has a structure of a Hopf algebra defined by the 4-term relations if m ≥ 3. We describe a relation of between the cohomology of this loop space and the set of finite type invariants for the pure braid group with n strands. Based on this we give expressions of certain link invariants as integrals over cycles of the above loop space. AMS Classification 55P35; 20F36, 57M27

Loop spaces of configuration spaces and finite type invariants