Loop spaces of configuration spaces and finite type invariants
Abstract
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 4term 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2002
 arXiv:
 arXiv:math/0211056
 Bibcode:
 2002math.....11056K
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology;
 55P35;
 20F36;
 57M27
 EPrint:
 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 149