Difference between revisions of "Knotted sphere"
From Encyclopedia of Mathematics
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| − | A non-trivial [[Two-dimensional knot|two-dimensional knot]] in the | + | {{TEX|done}} |
| + | A non-trivial [[Two-dimensional knot|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|Knot and link groups]]). | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> R.H. Crowell, R.H. Fox, "Introduction to knot theory" , Ginn (1963)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> R.H. Crowell, R.H. Fox, "Introduction to knot theory" , Ginn (1963)</TD></TR></table> | ||
Latest revision as of 08:37, 12 April 2014
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
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