Loop spaces of configuration spaces and finite type invariants

Details Loop spaces of configuration spaces and finite type invariants Loop spaces of configuration spaces and finite type invariants

2002-11-04

arxiv.org/abs/math/0211056v2

Geom. Topol. Monogr. 4 (2002) 143-160

Mathematics

Algebraic Topology

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper10.abs.html Version 2: correc

Scientific paper

The 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.

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