Loop spaces of configuration spaces and finite type invariants

Toshitake Kohno

Loop spaces of configuration spaces and finite type invariants

Algebraic Topology 2007-05-23 v2 Geometric Topology

Authors: Toshitake Kohno

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.

Keywords

loop spaces configuration spaces finite type invariants pure braid group hopf algebra link invariants

Cite

@article{arxiv.math/0211056,
  title  = {Loop spaces of configuration spaces and finite type invariants},
  author = {Toshitake Kohno},
  journal= {arXiv preprint arXiv:math/0211056},
  year   = {2007}
}

Comments

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

Loop spaces of configuration spaces and finite type invariants

Abstract

Keywords

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