28 citations · 94 across the 20 of their papers we have counts for
21 papers
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…
Integrality structures in topological strings and quantum -functions
Shengmao Zhu
In this article, we first prove the integrality of open string BPS numbers for a class of toric Calabi-Yau manifolds named generalized conifolds, by applying the method introduced…
On explicit formulae of LMOV invariants
Shengmao Zhu
We started a program to study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane) several years ago. This pape…
Solving equations with Hodge theory
Kefeng Liu, Shengmao Zhu
We treat two quite different problems related to changes of complex structures on Kähler manifolds by using global geometric method. First, by using operators from Hodge theory on…
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.
Topological strings, quiver varieties and Rogers-Ramanujan identities
Shengmao Zhu
Motivated by some recent works on BPS invariants of open strings/knot invariants, we guess there may be a general correspondence between the Ooguri-Vafa invariants of toric Calabi-…
Integrality structures in topological strings I: framed unknot
Wei Luo, Shengmao Zhu
We study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane). In this paper, we focus on the case of the resol…
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.
Volume conjecture for -invariants
Qingtao Chen, Kefeng Liu, Shengmao Zhu
This paper discuss an intrinsic relation among congruent relations \cite{CLPZ}, cyclotomic expansion and Volume Conjecture for invariants. Motivated by the congruent relati…
Full Colored HOMFLYPT Invariants, Composite Invariants and Congruent Skein Relation
Qingtao Chen, Shengmao Zhu
In this paper, we investigate the properties of the full colored HOMFLYPT invariants in the full skein of the annulus . We show that the full colored HOMFLYPT invarian…
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…
Hurwitz-Hodge integral identities from the cut-and-join equation
Wei Luo, Shengmao Zhu
In this paper, we present some Hurwitz-Hodge integral identities which are derived from the Laplace transform of the cut-and-join equation for the orbifold Hurwitz numbers. As an a…
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…
On a proof of the Bouchard-Sulkowski conjecture
Shengmao Zhu
In this short note, we give a proof of the free energy part of the BKMP conjecture of C^3 proposed by Bouchard and Sulkowski [4]. Hence the proof of the full BKMP conjecture for th…
The higher order terms in asymptotic expansion of color Jones polynomials
Shengmao Zhu
Color Jones polynomial is one of the most important quantum invariants in knot theory. Finding the geometric information from the color Jones polynomial is an interesting topic. In…
The Laplace transform of the cut-and-join equation of Mariño-Vafa formula and its applications
Shengmao Zhu
By the same method introduced in [9], we calculate the Laplace transform of the celebrated cut-and-join equation of Mariño-Vafa formula discovered by C. Liu, K. Liu and J. Zhou [17…