Geodesic
A Remark on the Realization of Mappings of the 3-Dimensional Sphere into Itself
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 10-14 
P. M. Akhmet'ev. A Remark on the Realization of Mappings of the 3-Dimensional Sphere into Itself. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 10-14. http://geodesic.mathdoc.fr/item/TM_2004_247_a1/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The problem of realizing a mapping $f\colon S^3 \to S^3$ of the $3$-dimensional sphere into itself in the ambient space $\mathbb R^6$ is reformulated in elementary terms. It is proved that, for $n=1,3,7$, there exists an equivariant mapping $F\colon S^n\times S^n\to S^n\times S^n$ such that a formal obstruction to its realization in $\mathbb R^{2n}$ is nontrivial.

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