Difference between revisions of "Conway skein triple"
From Encyclopedia of Mathematics
(Importing text file) |
m (OldImage template added) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
| − | Three oriented link diagrams, or tangle diagrams, | + | {{TEX|done}} |
| + | Three oriented link diagrams, or tangle diagrams, $L_+$, $L_-$, $L_0$ in $\mathbf R^3$, or more generally, in any [[Three-dimensional manifold|three-dimensional manifold]], that are the same outside a small ball and in the ball look like | ||
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240a.gif" /> | <img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240a.gif" /> | ||
| Line 5: | Line 6: | ||
Figure: c130240a | Figure: c130240a | ||
| − | Similarly one can define the Kauffman bracket skein triple of non-oriented diagrams | + | Similarly one can define the Kauffman bracket skein triple of non-oriented diagrams $L_+$, $L_0$ and $L_\infty$, and the Kauffman skein quadruple, $L_+$, $L_-$, $L_0$ and $L_\infty$, used to define the [[Brandt–Lickorish–Millett–Ho polynomial|Brandt–Lickorish–Millett–Ho polynomial]] and the [[Kauffman polynomial|Kauffman polynomial]]: |
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240b.gif" /> | <img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c130240b.gif" /> | ||
| Line 11: | Line 12: | ||
Figure: c130240b | Figure: c130240b | ||
| − | Generally, a skein set is composed of a finite number of | + | Generally, a skein set is composed of a finite number of $k$-tangles and can be used to build link invariants and skein modules (cf. also [[Skein module|Skein module]]). |
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> J.H. Conway, "An enumeration of knots and links" J. Leech (ed.), ''Computational Problems in Abstract Algebra'' , Pergamon (1969) pp. 329–358</TD></TR> | ||
| + | </table> | ||
| + | |||
| + | {{OldImage}} | ||
Latest revision as of 10:58, 26 March 2023
Three oriented link diagrams, or tangle diagrams, $L_+$, $L_-$, $L_0$ in $\mathbf R^3$, or more generally, in any three-dimensional manifold, that are the same outside a small ball and in the ball look like
Figure: c130240a
Similarly one can define the Kauffman bracket skein triple of non-oriented diagrams $L_+$, $L_0$ and $L_\infty$, and the Kauffman skein quadruple, $L_+$, $L_-$, $L_0$ and $L_\infty$, used to define the Brandt–Lickorish–Millett–Ho polynomial and the Kauffman polynomial:
Figure: c130240b
Generally, a skein set is composed of a finite number of $k$-tangles and can be used to build link invariants and skein modules (cf. also Skein module).
References
| [a1] | J.H. Conway, "An enumeration of knots and links" J. Leech (ed.), Computational Problems in Abstract Algebra , Pergamon (1969) pp. 329–358 |
🛠️ This page contains images that should be replaced by better images in the SVG file format. 🛠️
How to Cite This Entry:
Conway skein triple. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conway_skein_triple&oldid=14693
Conway skein triple. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conway_skein_triple&oldid=14693
This article was adapted from an original article by Jozef Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article