# Listing knot

From Encyclopedia of Mathematics

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) |

#### Comments

#### References

[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: http://encyclopediaofmath.org/index.php?title=Listing_knot&oldid=31597

This article was adapted from an original article by M.Sh. Farber (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article