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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1973 Volume 90(132), Number 2, Pages 173–183 (Mi sm3003)

This article is cited in 5 papers

Local knotting of submanifolds

O. Ya. Viro


Abstract: In this paper the author investigates the modification of the fundamental group of the complement of a submanifold of codimension 2 by knotting in a neighborhood of one of its points. With the aid of such knotting he constructs closed nonorientable surfaces in $\mathbf R^4$ with finite noncommutative groups. In the appendix he constructs a nontrivial knot such that, knotting by means of it does not change the type of the simplest imbedding $\mathbf RP^2\to\mathbf R^4$.
Figures: 6.
Bibliography: 10 titles.

UDC: 513.838

MSC: Primary 55A25, 55A05; Secondary 55A10

Received: 07.02.1972


 English version:
Mathematics of the USSR-Sbornik, 1973, 19:2, 166–176

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