Rational maps from Euclidean configuration spaces to spheres

Abstract

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mappingspaces $map(F(R^m,k),S^n)$ and $mapast(F(R^m,k),S^n)$ An explicit description of these spaces is given for k = 3. Thegeneral case for n odd is also presented as an immediate consequence of the rational version of a classical result of Thom.