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.
Keywords
loop space, configuration space, finite
type invariants, braid group, iterated integral