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Homotopy graph-complex for configuration and knot spaces


Authors: Pascal Lambrechts and Victor Turchin
Journal: Trans. Amer. Math. Soc. 361 (2009), 207-222
MSC (2000): Primary 57Q45; Secondary 55P62, 57R40
DOI: https://doi.org/10.1090/S0002-9947-08-04650-3
Published electronically: July 30, 2008
MathSciNet review: 2439404
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Abstract: We prove that the primitive part of the Sinha homology spectral sequence $ E^2$-term for the space of long knots is rationally isomorphic to the homotopy $ \mathcal{E}^2$-term. We also define natural graph-complexes computing the rational homotopy of configuration and of knot spaces.


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Additional Information

Pascal Lambrechts
Affiliation: Institut Mathématique, University Catholique de Louvain, 2 Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium
Email: lambrechts@math.ucl.ac.be

Victor Turchin
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403 – and – Institut des Hautes Études Scientifiques, 91440 Bures-sur-Yvette, France
Address at time of publication: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: turchin@math.ksu.edu

DOI: https://doi.org/10.1090/S0002-9947-08-04650-3
Keywords: Knot spaces, embedding calculus, Bousfield-Kan spectral sequence, graph-complexes
Received by editor(s): November 27, 2006
Published electronically: July 30, 2008
Additional Notes: The first author is chercheur qualifié au F.N.R.S
The second author was supported in part by the grants NSH-1972.2003.01 and RFBR 05-01-01012a.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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