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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

Loop spaces of configuration spaces and finite type invariants

Toshitake Kohno

Geometry & Topology Monographs 4 (2002) 143–160

DOI: 10.2140/gtm.2002.4.143

Abstract

The total homology of the loop space of the configuration space of ordered distinct n points in Rm has a structure of a Hopf algebra defined by the 4–term relations if m≥3. 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 space, configuration space, finite type invariants, braid group, iterated integral

Mathematical Subject Classification

Primary: 55P35

Secondary: 20F36, 57M27

References
Publication

Received: 19 December 2001
Revised: 9 April 2002
Accepted: 22 July 2002
Published: 19 September 2002

Authors
Toshitake Kohno
Graduate School of Mathematical Sciences
University of Tokyo
Tokyo 153-8914
Japan