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A geometric realization of \(C\)-groups. (English. Russian original) Zbl 0842.57018

Russ. Acad. Sci., Izv., Math. 45, No. 1, 197-206 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 4, 194-203 (1994).
The author proves that for any \(C\)-group \(G\) and for any \(n \geq 2\) there exists a non-singular \(n\)-dimensional compact orientable manifold without boundary \(X_n \subset S^{n + 2}\), such that \(\pi_1(S^{n + 2} \setminus X_n) \approx G\). Moreover, the author generalizes to the \(n\)-dimensional case the known representations of Riemannian surfaces \((n =2)\) in the form of a finite number of pasted Riemann spheres with cuts.

MSC:

57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
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