"Linking number"의 두 판 사이의 차이

2021년 2월 17일 (수) 02:04 기준 최신판

linking number and HOMFLY polynomial

Let \(L\) be a link.
\(P_L\) denote the HOMFLY polynomial
recall that \(P_L(a,z)\in \mathbb[a^{\pm 1}, z^{\pm 1}]\) satisfies the skein relation

\[ aP_{L_{+}} - a^{-1}P_{L_{-}}=zP_{L_0} \] and \[ P_{n-unlink}=\left(\frac{a-a^{-1}}{z}\right)^{n-1} \]

thm (Sikora)

For any link \(L\) of \(n\) components the limit \[ Q_L(q) : = \lim_{v\to 1} \left(\frac{q}{a-a^{-1}}\right)^{\frac{n-1}{2}}P_L(a,\sqrt{q(a-a^{-1})}) \] exists.

\(Q_L(q)\) is a polynomial in \(q\) and \(Q_L(q)=\sum c_i(L)q^i\)

Birman
- two 3-braids whose closures have the same Homfly-pt polynomial but different linking numbers between their components
- pair of links with the same HOMFLYPT polynomial but different linking matrix

related items

HOMFLY polynomial

expositions

Sikora, Note on the Homfly-pt polynomial and linking numbers

메타데이터

위키데이터

ID : Q2000614

Spacy 패턴 목록

[{'LOWER': 'linking'}, {'LEMMA': 'number'}]

@@ 1번째 줄: / 1번째 줄: @@
 ==linking number and HOMFLY polynomial==
-* Let $L$ be a link.
+* Let <math>L</math> be a link.
-* $P_L$ denote the HOMFLY polynomial
+* <math>P_L</math> denote the HOMFLY polynomial
-* recall that $P_L(a,z)\in \mathbb[a^{\pm 1}, z^{\pm 1}]$ satisfies the skein relation
+* recall that <math>P_L(a,z)\in \mathbb[a^{\pm 1}, z^{\pm 1}]</math> satisfies the skein relation
 :<math>
 aP_{L_{+}} - a^{-1}P_{L_{-}}=zP_{L_0}
 </math>
 and
-$$
+:<math>
 P_{n-unlink}=\left(\frac{a-a^{-1}}{z}\right)^{n-1}
-$$
+</math>
 ;thm (Sikora)
-For any link $L$ of $n$ components the limit
+For any link <math>L</math> of <math>n</math> components the limit
-$$
+:<math>
 Q_L(q) : = \lim_{v\to 1} \left(\frac{q}{a-a^{-1}}\right)^{\frac{n-1}{2}}P_L(a,\sqrt{q(a-a^{-1})})
-$$
+</math>
 exists.
-$Q_L(q)$ is a polynomial in $q$ and $Q_L(q)=\sum c_i(L)q^i$
+<math>Q_L(q)</math> is a polynomial in <math>q</math> and <math>Q_L(q)=\sum c_i(L)q^i</math>
+* Birman
+** two 3-braids whose closures have the same Homfly-pt polynomial but different linking numbers between their components
+** pair of links with the same HOMFLYPT polynomial but different linking matrix
 ==related items==
@@ 28번째 줄: / 32번째 줄: @@
 ==expositions==
 * [http://www.math.buffalo.edu/~asikora/Papers/lk.pdf Sikora, Note on the Homfly-pt polynomial and linking numbers]
+[[분류:Knot theory]]
+[[분류:migrate]]
+==메타데이터==
+===위키데이터===
+* ID :  [https://www.wikidata.org/wiki/Q2000614 Q2000614]
+===Spacy 패턴 목록===
+* [{'LOWER': 'linking'}, {'LEMMA': 'number'}]