28 citations · 94 across the 20 of their papers we have counts for
10 papers · 1 filter
A proof of the framed LMOV conjecture for links
Kefeng Liu, Pan Peng, Shengmao Zhu
We prove the Labastida--Mariño--Ooguri--Vafa conjecture for oriented links with arbitrary integer framings. Consequently, the framed reformulated invariants have finite integral LM…
Cyclotomic expansions for double twist knots with an odd number of half-twists
Qingtao Chen, Kefeng Liu, Shengmao Zhu
In this note, we compute the cyclotomic expansion formula for colored Jones polynomial of double twist knots with an odd number of half-twists by usin…
On the asymptotic expansions of various quantum invariants II: the colored Jones polynomial of twist knots at the root of unity and
Qingtao Chen, Shengmao Zhu
This is the second article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this article, following the me…
Cyclotomic expansions for the colored HOMFLY-PT invariants of double twist knots
Qingtao Chen, Kefeng Liu, Shengmao Zhu
In this short note, we prove the cyclotomic expansion formula for the colored HOMFLY-PT invariant of double twist knots, it confirms the cyclotomic expansion conjecture for …
Integrality of the LMOV invariants for framed unknot
Wei Luo, Shengmao Zhu
The Labastida-Marinõ-Ooguri-Vafa (LMOV) invariants are the open string BPS invariants which are expected to be integers based on the string duality conjecture from M-theory. Severa…
New structures for colored HOMFLY-PT invariants
Shengmao Zhu
In this paper, we present several new structures for the colored HOMFLY-PT invariants of framed links. First, we prove the strong integrality property for the normalized colored HO…
A new approach to Lickorish-Millett type formulae
Xin Zhou, Shengmao Zhu
In this paper, we introduce a new method to prove the Lickorish-Millett type formulae for colored HOMFLY-PT polynomials of links.
A simple proof of the strong integrality for full colored HOMFLYPT invariants
Shengmao Zhu
By using the HOMFLY skein theory. We prove a strong integrality theorem for the reduced colored HOMFLYPT invariants defined by a basis in the full HOMFLY skein of the annulus.
Congruent skein relations for colored HOMFLY-PT invariants and colored Jones polynomials
Qingtao Chen, Kefeng Liu, Pan Peng +1
Colored HOMFLY-PT invariant, the generalization of the colored Jones polynomial, is one of the most important quantum invariants of links. This paper is devoted to investigating th…
Colored HOMFLY polynomial via skein theory
Shengmao Zhu
In this paper, we study the properties of the colored HOMFLY polynomials via HOMFLY skein theory. We prove some limit behaviors and symmetries of the colored HOMFLY polynomial pred…