Difference between revisions of "Listing knot"
From Encyclopedia of Mathematics
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| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.B. Listing, "Vorstudien zur Topologie" , Göttingen (1847)</TD></TR></table> | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.B. Listing, "Vorstudien zur Topologie" , Göttingen (1847)</TD></TR> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> R.H. Crowell, R.H. Fox, "Introduction to knot theory" , Ginn (1963)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> L.H. Kauffman, "On knots" , Princeton Univ. Press (1987)</TD></TR></table> | ||
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Revision as of 06:35, 9 April 2023
One of the simplest non-trivial knots (see Fig. and Knot theory). A Listing knot is denoted by the symbol $4_1$ (see Knot table) and is sometimes called a figure 8 or fourfold knot. The group of the Listing knot (cf. Knot and link groups) has the presentation $|x,y\colon yx^{-1}yxy^{-1}=x^{-1}yxy^{-1}x|$, and the Alexander polynomial is $\Delta_1=t^2-3t+1$. It was considered by I.B. Listing [1].
Figure: l059730a
References
| [1] | I.B. Listing, "Vorstudien zur Topologie" , Göttingen (1847) |
| [a1] | R.H. Crowell, R.H. Fox, "Introduction to knot theory" , Ginn (1963) |
| [a2] | L.H. Kauffman, "On knots" , Princeton Univ. Press (1987) |
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How to Cite This Entry:
Listing knot. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Listing_knot&oldid=53697
Listing knot. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Listing_knot&oldid=53697
This article was adapted from an original article by M.Sh. Farber (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article