"Linking number"의 두 판 사이의 차이

둘러보기로 가기 검색하러 가기
(→‎메타데이터: 새 문단)
36번째 줄: 36번째 줄:
== 메타데이터 ==
* ID :  [https://www.wikidata.org/wiki/Q2000614 Q2000614]
* ID :  [https://www.wikidata.org/wiki/Q2000614 Q2000614]
===Spacy 패턴 목록===
* [{'LOWER': 'linking'}, {'LEMMA': 'number'}]

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




Spacy 패턴 목록

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