Rational maps from Euclidean Configuration Spaces to Spheres

Urtzi Buijs; Antonio Garvin; Aniceto Murillo

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arXiv · 1806.11565

Rational maps from Euclidean Configuration Spaces to Spheres

Urtzi Buijs·Antonio Garvin·Aniceto Murillo

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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), S^n)$ and $ map^*(F(\mathbb R^m,k), S^n)$. 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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Urtzi Buijs, Antonio Garvin, Aniceto Murillo. 2018-06-29. Rational maps from Euclidean Configuration Spaces to Spheres. https://arxiv.org/abs/1806.11565

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