Related papers: $\hat{Z}$ invariants at rational $\tau$
We propose the Volume Conjecture for the relative Reshetikhin-Turaev invariants of a closed oriented $3$-manifold with a colored framed link inside it whose asymptotic behavior is related to the volume and the Chern-Simons invariant of the…
We introduce supergroup analogues of 3-manifold invariants $\hat{Z}$, also known as homological blocks, which were previously considered for ordinary compact semisimple Lie groups. We focus on superunitary groups, and work out the case of…
In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds…
The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with Jones- Witten-Reshetikhin-Turaev invariant arising from Chern-Simons filed theory for the same Lie…
Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order…
By using the notion of a rigid R-matrix in a monoidal category and the Reshetikhin--Turaev functor on the category of tangles, we review the definition of the associated invariant of long knots. In the framework of the monoidal categories…
We derive series representations for the tau functions of the $q$-Painlev\'e V, $\mathrm{III_1}$, $\mathrm{III_2}$, and $\mathrm{III_3}$ equations, as degenerations of the tau functions of the $q$-Painlev\'e VI equation in [Jimbo M., Nagoya…
In this paper, we consider the Reshetikhin-Turaev invariants of knots in the three-sphere obtained from a twisted Drinfeld double of a Hopf algebra, or equivalently, the relative Drinfeld center of the crossed product…
For a K3 surface S, we study motivic invariants of stable pairs moduli spaces associated to 3-fold thickenings of S. We conjecture suitable deformation and divisibility invariances for the Betti realization. Our conjectures, together with…
A problem about Khovanov homology and 3-manifolds is discussed in this paper.
We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of links in L(p,q) as a function of the level r-2. They are given by 1 over the square root of r times one of p Laurent polynomials evaluated at e to the 2 pi i divided…
For an oriented finite volume hyperbolic 3-manifold M with a fixed spin structure \eta, we consider a sequence of invariants {\tau_n(M; \eta)}. Roughly speaking, {\tau_n(M; \eta)} is the Reidemeister torsion of M with respect to the…
The Turaev-Viro invariant is defined as a certain state sum calculated on an arbitrary simple spine of a 3-manifold. We specify each term of the sum as 0-term, 1-term or 2-term such that each sum of the terms having the same type is an…
We consider certain invariants of links in 3-manifolds, obtained by a specialization of the Turaev-Viro invariants of 3-manifolds, that we call colored Turaev-Viro invariants. Their construction is based on a presentation of a pair (M,L),…
The Yau-Zaslow conjecture determines the reduced genus 0 Gromov-Witten invariants of K3 surfaces in terms of the Dedekind eta function. Classical intersections of curves in the moduli of K3 surfaces with Noether-Lefschetz divisors are…
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm…
The main object of study in this paper is the completion Z[q]^N=\varprojlim_n Z[q]/((1-q)(1-q^2)...(1-q^n)) of the polynomial ring Z[q], which arises from the study of a new invariant of integral homology 3-spheres with values in Z[q]^N…
Gukov, Pei, Putrov, and Vafa developed a $q$-series invariant of negative definite plumbed $3$-manifolds with spin$^{c}$ structures, building on earlier work of Lawrence and Zagier. This was recently generalized to an an infinite family of…
In this paper, we study quantum modular forms in connection to quantum invariants of plumbed 3-manifolds introduced recently by Gukov, Pei, Putrov, and Vafa. We explicitly compute these invariants for any $3$-leg star plumbing graphs whose…
We propose a program for bridging the gap between the perturbative BV-BFV quantization of Chern-Simons theory and the non-perturbative Reshetikhin-Turaev (RT) invariants of 3-manifolds, passing through factorization homology of…