Rational maps from Euclidean Configuration Spaces to Spheres

Urtzi Buijs; Antonio Garvin; Aniceto Murillo

Rational maps from Euclidean Configuration Spaces to Spheres

Algebraic Topology 2018-07-02 v1

Authors: Urtzi Buijs , Antonio Garvin , Aniceto Murillo

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.

Keywords

rational maps algebraic topology homotopy groups

Cite

@article{arxiv.1806.11565,
  title  = {Rational maps from Euclidean Configuration Spaces to Spheres},
  author = {Urtzi Buijs and Antonio Garvin and Aniceto Murillo},
  journal= {arXiv preprint arXiv:1806.11565},
  year   = {2018}
}

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