Knotted sphere

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).

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