Rational maps from Euclidean Configuration Spaces to Spheres

2018/06/29 by Buijs, Urtzi, Garvin, Antonio, Murillo, Aniceto
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.11565

Abstract

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

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