Geodesic
On isotopic and discrete realizations of maps of an~$n$-dimensional sphere in Euclidean space
Sbornik. Mathematics, Tome 187 (1996) no. 7, pp. 951-980

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In this paper we consider questions of whether a compact space can be embedded in a Euclidean space. The problem of embedding an '$S^n$-like' compact space in $\mathbb R^{2n}$ is solved affirmatively under certain restrictions on the dimension $n$. We clarify the relations between the realization problem and areas of homotopy theory and differential topology. 
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     author = {P. M. Akhmet'ev},
     title = {On isotopic and discrete realizations of maps of an~$n$-dimensional sphere in {Euclidean} space},
     journal = {Sbornik. Mathematics},
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     volume = {187},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_7_a0/}
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P. M. Akhmet'ev. On isotopic and discrete realizations of maps of an~$n$-dimensional sphere in Euclidean space. Sbornik. Mathematics, Tome 187 (1996) no. 7, pp. 951-980. http://geodesic.mathdoc.fr/item/SM_1996_187_7_a0/