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On loop spaces of configuration spaces


Authors: F. R. Cohen and S. Gitler
Journal: Trans. Amer. Math. Soc. 354 (2002), 1705-1748
MSC (2000): Primary 20F14, 20F36, 52C35, 55P35, 14D99
DOI: https://doi.org/10.1090/S0002-9947-02-02948-3
Published electronically: January 11, 2002
MathSciNet review: 1881013
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Abstract: This article gives an analysis of topological and homological properties for loop spaces of configuration spaces. The main topological results are given by certain choices of product decompositions of these spaces, as well as ``twistings" between the factors. The main homological results are given in terms of extensions of the ``infinitesimal braid relations" or ``universal Yang-Baxter Lie relations".


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Additional Information

F. R. Cohen
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: cohf@math.rochester.edu

S. Gitler
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627, and Departamento de Matemáticas, Cinvestav, Apdo. Postal 14-740 , México, D.F. 07300
Email: sgitler@math.cinvestav.mx

DOI: https://doi.org/10.1090/S0002-9947-02-02948-3
Keywords: Braid groups, configuration spaces, descending central series, loop spaces
Received by editor(s): October 12, 1999
Received by editor(s) in revised form: September 1, 2001
Published electronically: January 11, 2002
Additional Notes: The authors were partially supported by the National Science Foundation Grant number 9704410.
Article copyright: © Copyright 2002 American Mathematical Society