Loop spaces of configuration spaces and finite type invariants

2002/11/30 by Toshitake Kohno
Mathematics · #math.AT #math.GT #msc:55P35 #msc:20F36 #msc:57M27

paper · pdf

published as Geom. Topol. Monogr. 4 (2002) 143-160 · 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

arxiv created 2003/09/09 · arxiv updated 2009/11/30

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 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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