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Knotted sphere

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A non-trivial two-dimensional knot in the $4$-dimensional Euclidean space $E^4$; a sphere $S^2$ which cannot be obtained by rotation in $E^4$ of a knotted arc $k$ situated in the half-space $E_+^3$ around the plane bounding the half-space. The fundamental group $\pi(E^4\setminus S^2)$ of a knotted sphere is not a knot group (cf. Knot and link groups).

References

[1] R.H. Crowell, R.H. Fox, "Introduction to knot theory" , Ginn (1963)
How to Cite This Entry:
Knotted sphere. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Knotted_sphere&oldid=12342
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article