Listing knot

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].

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l059730a.gif" />

Figure: l059730a

Listing knot projection

Listing knot projection

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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