The rational homotopy type of configuration spaces of two points

Pascal Lambrechts[1]; Don Stanley

  • [1] Université de Louvain, Institut Mathématique, 2 chemin du Cyclotron, 1348 Louvain-la-Neuve, (Belgique), University of Ottawa, Department of Mathematics and Statistics, 585 King Edward Ave., Ottawa, ON K1N 6N5 (CANADA)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 4, page 1029-1052
  • ISSN: 0373-0956

Abstract

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We prove that the rational homotopy type of the configuration space of two points in a 2 -connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.

How to cite

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Lambrechts, Pascal, and Stanley, Don. "The rational homotopy type of configuration spaces of two points." Annales de l’institut Fourier 54.4 (2004): 1029-1052. <http://eudml.org/doc/116129>.

@article{Lambrechts2004,
abstract = {We prove that the rational homotopy type of the configuration space of two points in a $2$-connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.},
affiliation = {Université de Louvain, Institut Mathématique, 2 chemin du Cyclotron, 1348 Louvain-la-Neuve, (Belgique), University of Ottawa, Department of Mathematics and Statistics, 585 King Edward Ave., Ottawa, ON K1N 6N5 (CANADA)},
author = {Lambrechts, Pascal, Stanley, Don},
journal = {Annales de l’institut Fourier},
keywords = {configuration space; Sullivan model; rational homotopy type; Sullivan theory; CDGA-model; formal},
language = {eng},
number = {4},
pages = {1029-1052},
publisher = {Association des Annales de l'Institut Fourier},
title = {The rational homotopy type of configuration spaces of two points},
url = {http://eudml.org/doc/116129},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Lambrechts, Pascal
AU - Stanley, Don
TI - The rational homotopy type of configuration spaces of two points
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 4
SP - 1029
EP - 1052
AB - We prove that the rational homotopy type of the configuration space of two points in a $2$-connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.
LA - eng
KW - configuration space; Sullivan model; rational homotopy type; Sullivan theory; CDGA-model; formal
UR - http://eudml.org/doc/116129
ER -

References

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  8. P. Lambrechts, Cochain model for thickenings and its application to rational LS-category, Manuscripta Math 103 (2000), 143-160 Zbl0964.55013MR1796311
  9. P. Lambrechts, D. Stanley, Algebraic models of the complement of a subpolyhedron in a closed manifold (submitted) 
  10. P. Lambrechts, D. Stanley, D G module models for the configuration space of k points (in preparation) Zbl1069.55006
  11. N. Levitt, Spaces of arcs and configuration spaces of manifolds, Topology 34 (1995), 217-230 Zbl0845.57021MR1308497
  12. J. Milnor, D. Husemoller, Symmetric bilinear forms, Band 73 (1973), Springer-Verlag Zbl0292.10016MR506372
  13. B. Totaro, Configuration spaces of algebraic varieties, Topology 35 (1996), 1057-1067 Zbl0857.57025MR1404924
  14. J. Stasheff, Rational Poincaré duality spaces, Illinois J. Math 27 (1983), 104-109 Zbl0488.55010MR684544
  15. D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977), 269-331 Zbl0374.57002MR646078

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