Listing knot

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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


[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)
How to Cite This Entry:
Listing knot. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.Sh. Farber (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article