View source for Listing knot

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One of the simplest non-trivial knots (see Fig. and [[Knot theory|Knot theory]]). A Listing knot is denoted by the symbol $4_1$ (see [[Knot table|Knot table]]) and is sometimes called a figure 8 or fourfold knot. The group of the Listing knot (cf. [[Knot and link groups|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 [[#References|[1]]].

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

Figure: l059730a

====References====
<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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