Homotopy type of Euclidean configuration spaces

Salvatore, Paolo

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

Résumé

Let $F({\mathbb {R}}^n, k)$ denote the configuration space of pairwise-disjoint $k$-tuples of points in ${\mathbb {R}}^n$. In this short note the author describes a cellular structure for $F({\mathbb {R}}^n, k)$ when $n \ge 3$. 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 $F({\mathbb {R}}^n, k)$ is well-understood. This allows an identification of the location of the cells of $F({\mathbb {R}}^n, k)$ 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.

Détail

MR MR1826689 | Zbl 0974.55003

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