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.

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},
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
UR - http://eudml.org/doc/116129
ER -

References

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  1. F. Cohen, L. Taylor, Computations of Gelfand-Fuks cohomology, the cohomology of function spaces, and the cohomology of configuration spaces, Geometric applications of homotopy theory I (Proc. Conf., Evanston 1977) 657 (1978), 106-143, Springer, Berlin Zbl0398.55004
  2. P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math 29 (1975), 245-274 Zbl0312.55011MR382702
  3. Y. Félix, S. Halperin, J.-C. Thomas, Rational homotopy theory, vol. 210 (2001), Springer-Verlag Zbl0961.55002MR1802847
  4. W. Fulton, R. Mac Pherson, A compactification of configuration spaces, Annals of Math 139 (1994), 183-225 Zbl0820.14037MR1259368
  5. J. Klein, Poincaré duality embeddings and fiberwise homotopy theory, Topology 38 (1999), 597-620 Zbl0928.57028MR1670412
  6. J. Klein, Poincaré duality embeddings and fiberwise homotopy theory, II, Quart. Jour. Math. Oxford 53 (2002), 319-335 Zbl1030.57036MR1930266
  7. I. Kriz, On the rational homotopy type of configuration spaces, Annals of Math 139 (1994), 227-237 Zbl0829.55008MR1274092
  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) 
  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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