This article is cited in 21 papers

On isotopic and discrete realizations of maps of an $n$-dimensional sphere in Euclidean space

P. M. Akhmet'ev

Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation

Abstract: 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.

UDC: 515.164

MSC: Primary 58C27; Secondary 32S45

Received: 01.11.1994

DOI: 10.4213/sm142

 English version: Sbornik: Mathematics, 1996, 187:7, 951–980

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