2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65534The total homology of the loop space of the configuration space of ordered distinct n points in R^m has a structure of a Hopf algebra defined by the 4-term relations if m>2. 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.Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper10.abs.html Version 2: corrections to superscripts on pages 148 and 149Algebraic TopologyGeometric Topology55P35, 20F36, 57M27text