查看“︁考夫曼多項式”︁的源代码

在[[紐結理論|纽结理论]]中，'''考夫曼多项式（Kauffman polynomial）'''是二元纽结多项式。<ref>{{Cite journal|title=An invariant of regular isotopy|url=http://homepages.math.uic.edu/~kauffman/IRH.pdf|last=Kauffman|first=Louis|authorlink=Louis Kauffman|date=1990|journal=[[Transactions of the American Mathematical Society]]|issue=2|doi=10.1090/S0002-9947-1990-0958895-7|volume=318|pages=417–471|mr=0958895|access-date=2020-03-07|archive-date=2021-05-06|archive-url=https://web.archive.org/web/20210506174649/http://homepages.math.uic.edu/~kauffman/IRH.pdf}}</ref> 

<math>F(K)(a,z)=a^{-w(K)}L(K)\,</math>

<math>w(K)</math> 是[[绞拧数]]，<math>L(K)</math> 的定义是：

* <math>L(O) = 1</math> (O是[[平凡纽结]]).
* <math>L(s_r)=aL(s), \qquad L(s_\ell)=a^{-1}L(s).</math>
* 通过第2和3的[[Reidemeister变换]]，L不变

L满足考夫曼的[[糾結關係]]：

[[File:Kauffman_poly.png|链接=https://zh.wikipedia.org/wiki/File:Kauffman_poly.png|400x400像素]]

[[琼斯多项式]]是考夫曼多項式的特烈（ ''L'' 成为[[括號多項式]]）。SO(n)的[[陈-西蒙斯理论]]给予夫曼多項式，SU(n)陈西理论给予[[HOMFLY多項式|HOMFLY多项式]]。<ref>{{Cite journal|title=Quantum field theory and the Jones polynomial|url=https://projecteuclid.org/euclid.cmp/1104178138|last=Witten|first=Edward|authorlink=Edward Witten|date=1989|journal=[[Communications in Mathematical Physics]]|issue=3|doi=10.1007/BF01217730|volume=121|pages=351–399|mr=0990772|access-date=2020-03-07|archive-date=2020-11-01|archive-url=https://web.archive.org/web/20201101010542/https://projecteuclid.org/euclid.cmp/1104178138}}</ref>

== 参考文献 ==
{{Reflist}}

== 阅读 ==

* {{Cite book|last=Kauffman|first=Louis|authorlink=Louis Kauffman|title=On Knots|year=1987|isbn=0-691-08435-1|series=Annals of Mathematics Studies|volume=115|publisher=[[Princeton University Press]]|location=Princeton, NJ|mr=0907872}}

{{纽结理论}}
[[Category:陈-西蒙斯理论]]
[[Category:纽结理论]]