Linking number - 편집 역사

2021년 2월 17일 (수) 10:04에 Pythagoras0님의 편집

2021-02-17T10:04:05Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T08:18:35Z

메타데이터: 새 문단

2020년 11월 16일 (월) 12:27에 Pythagoras0님의 편집

2020-11-16T12:27:30Z

2020년 11월 13일 (금) 09:52에 imported>Pythagoras0님의 편집

2020-11-13T09:52:56Z

imported>Pythagoras0: /* linking number and HOMFLY polynomial */

2017-05-24T07:34:42Z

linking number and HOMFLY polynomial

imported>Pythagoras0: /* expositions */

2017-05-24T06:00:19Z

expositions

2017년 5월 24일 (수) 05:59에 imported>Pythagoras0님의 편집

2017-05-24T05:59:57Z

imported>Pythagoras0: 새 문서: ==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 relat...

2017-05-24T05:58:57Z

새 문서: ==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 relat...

새 문서

==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
:<math>
aP_{L_{+}} - a^{-1}P_{L_{-}}=zP_{L_0}
</math>
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 $Q_L(q)=\sum c_i(L)q^i$

@@ 36번째 줄: / 36번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q2000614 Q2000614]

← 이전 판		2020년 12월 28일 (월) 08:18 판
35번째 줄:		35번째 줄:
	[[분류:Knot theory]]		[[분류:Knot theory]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q2000614 Q2000614]

← 이전 판		2020년 11월 13일 (금) 09:52 판
34번째 줄:		34번째 줄:

	[[분류:Knot theory]]		[[분류:Knot theory]]
		+	[[분류:migrate]]

← 이전 판		2017년 5월 24일 (수) 07:34 판
21번째 줄:		21번째 줄:
	$Q_L(q)$ is a polynomial in $q$ and $Q_L(q)=\sum c_i(L)q^i$		$Q_L(q)$ 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==		==related items==

← 이전 판		2017년 5월 24일 (수) 06:00 판
28번째 줄:		28번째 줄:
	==expositions==		==expositions==
	* [http://www.math.buffalo.edu/~asikora/Papers/lk.pdf Sikora, Note on the Homfly-pt polynomial and linking numbers]		* [http://www.math.buffalo.edu/~asikora/Papers/lk.pdf Sikora, Note on the Homfly-pt polynomial and linking numbers]
		+
		+	[[분류:Knot theory]]

@@ 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>

← 이전 판		2017년 5월 24일 (수) 05:59 판
20번째 줄:		20번째 줄:

	$Q_L(q)$ is a polynomial in $q$ and $Q_L(q)=\sum c_i(L)q^i$		$Q_L(q)$ is a polynomial in $q$ and $Q_L(q)=\sum c_i(L)q^i$
		+
		+
		+	==related items==
		+	* [[HOMFLY polynomial]]
		+
		+
		+	==expositions==
		+	* [http://www.math.buffalo.edu/~asikora/Papers/lk.pdf Sikora, Note on the Homfly-pt polynomial and linking numbers]