2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226075We calculate the Lusternik-Schnirelmann category of the k-th ordered configuration spaces F(R^n,k) of R^n and give bounds for the category of the corresponding unordered configuration spaces B(R^n,k) and the sectional category of the fibrations pi^n_k: F(R^n,k) --> B(R^n,k). We show that secat(pi^n_k) can be expressed in terms of subspace category. In many cases, eg, if n is a power of 2, we determine cat(B(R^n,k)) and secat(pi^n_k) precisely.This is the version published by Geometry & Topology Monographs on 19 March 2008Algebraic TopologyGeneral Topology55M30, 55R80, 55S40text