Homotopy type of Euclidean configuration spaces

Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books, (2001), p. 161-164 / Harvested from

Résumé

Let $F (ℝ^{n}, k)$ denote the configuration space of pairwise-disjoint $k$ -tuples of points in $ℝ^{n}$ . In this short note the author describes a cellular structure for $F (ℝ^{n}, k)$ when $n \geq 3$ . From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of $F (ℝ^{n}, k)$ is well-understood. This allows an identification of the location of the cells of $F (ℝ^{n}, k)$ in a minimal cell decomposition. Somewhat more detail is provided by the main result here, in which the attaching maps are identified as higher order Whitehead products.

MR MR1826689 | Zbl 0974.55003

EUDML-ID : urn:eudml:doc:221510
Mots clés:

@article{701676,
     title = {Homotopy type of Euclidean configuration spaces},
     booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2001},
     pages = {161-164},
     mrnumber = {MR1826689},
     zbl = {0974.55003},
     url = {http://dml.mathdoc.fr/item/701676}
}

Salvatore, Paolo. Homotopy type of Euclidean configuration spaces, dans Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books,  (2001), pp. 161-164. http://gdmltest.u-ga.fr/item/701676/