Orthogonal quantum group invariants of links

Lin Chen, Qingtao Chen

Research output: Contribution to journalArticle

Abstract

We first study the Chern-Simons partition function of orthogonal quantum group invariants and then propose a new orthogonal Labastida-Mariño- Ooguri-Vafa (LMOV) conjecture as well as a degree conjecture for free energy associated to the orthogonal Chern-Simons partition function. We prove the degree conjecture and some interesting cases of the orthogonal LMOV conjecture. In particular, we provide a formula of the colored Kauffman polynomials for torus knots and links, and applied this formula to verify certain cases of the conjecture at roots of unity except 1. We also derive formulas of Lickorish-Millett type for Kauffman polynomials and relate all these to the orthogonal LMOV conjecture.

Original languageEnglish (US)
Pages (from-to)267-318
Number of pages52
JournalPacific Journal of Mathematics
Volume257
Issue number2
DOIs
StatePublished - Jan 1 2012

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Orthogonal Group
Quantum Groups
Invariant
Kauffman Polynomial
Partition Function
Torus knot
Roots of Unity
Free Energy
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Keywords

  • Quantum invariant

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Orthogonal quantum group invariants of links. / Chen, Lin; Chen, Qingtao.

In: Pacific Journal of Mathematics, Vol. 257, No. 2, 01.01.2012, p. 267-318.

Research output: Contribution to journalArticle

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