Namespaces
Variants
Actions

Difference between revisions of "Listing knot"

From Encyclopedia of Mathematics
Jump to: navigation, search
(TeX)
(gather refs)
Line 7: Line 7:
  
 
====References====
 
====References====
<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>
  
 
+
{{OldImage}}
 
 
====Comments====
 
 
 
 
 
====References====
 
<table><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>
 

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)


🛠️ This page contains images that should be replaced by better images in the SVG file format. 🛠️
How to Cite This Entry:
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