Related papers: Turaev-Viro invariant from the modular double of $…

We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn filling. This leads to two-sided bounds on the volume of…

We define a relative version of the Turaev-Viro invariants for an ideally triangulated compact 3-manifold with non-empty boundary and a coloring on the edges, generalizing the Turaev-Viro invariants [35] of the manifold. We also propose the…

We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic $3$-manifold, evaluated at the root of unity $\exp({2\pi\sqrt{-1}}/{r})$ instead of the standard $\exp({\pi\sqrt{-1}}/{r})$. We present…

We establish a relation between the "large r" asymptotics of the Turaev-Viro invariants $TV_r$ and the Gromov norm of 3-manifolds. We show that for any orientable, compact 3-manifold $M$, with (possibly empty) toroidal boundary, $\log |TV_r…

Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum…

In this paper, we show that the Turaev-Viro invariant volume conjecture posed by Chen and Yang is preserved under gluings of toroidal boundary components for a family of $3$-manifolds. In particular, we show that the asymptotics of the…

We establish the geometry behind the quantum $6j$-symbols under only the admissibility conditions as in the definition of the Turaev-Viro invariants of $3$-manifolds. As a classification, we show that the $6$-tuples in the quantum…

We describe the simplest non-trivial modular category $\mathfrak{E}$ with two simple objects. Then we extract from this category the invariant for non-oriented links in 3-sphere and two invariants for 3-manifolds: the complex-valued Turaev…

Andersen, Masbaum and Ueno conjectured that certain quantum representations of surface mapping class groups should send pseudo-Anosov mapping classes to elements of infinite order (for large enough level $r$). In this paper, we relate the…

We conjecture an upper bound on the growth of the Yokota invariant of polyhedral graphs, extending a previous result on the growth of the $6j$-symbol. Using Barrett's Fourier transform we are able to prove this conjecture in a large family…

In 2015, Chen and Yang proposed a volume conjecture that stated that certain Turaev-Viro invariants of an hyperbolic 3-manifold should grow exponentially with a rate equal to the hyperbolic volume. Since then, this conjecture has been…

The Turaev-Viro state sum invariant can be extended to 3-manifolds with free boundaries. We use this fact to describe generalized Frobenius-Schur indicators as Turaev-Viro invariants of solid tori. This provides a geometric understanding of…

We give a closed formula for volumes of generic hyperbolic tetrahedra in terms of edge lengths. The cue of our formula is by the volume conjecture for the Turaev-Viro invariant of closed 3-manifolds, which is defined from the quantum…

We show how the Turaev--Viro invariant can be understood within the framework of Chern--Simons theory with gauge group SU(2). We also describe a new invariant for certain class of graphs by interpreting the triangulation of a manifold as a…

We study the large $r$ asymptotic behaviour of the Turaev-Viro invariants of oriented Seifert fibered 3-manifolds at the root $q=e^\frac{2\pi i}{r}$. As an application, we prove the volume conjecture for large families of oriented Seifert…

We show that the renormalized quantum invariants of links and graphs in the 3-sphere, derived from tensor categories in ["Modified quantum dimensions and re-normalized link invariants", arXiv:0711.4229] lead to modified 6j-symbols and to…

We prove exact complexity dichotomies for two quantum invariants of closed oriented three-manifolds, with the categorical data fixed. For a modular category $\mathcal{C}$, computing the Reshetikhin--Turaev invariant $Z_{\mathcal{C}}(M)$…

We investigate the conjectural relations between the Reshetikhin-Turaev-Witten quantum SU(2) invariants and the volume of hyperbolic 3-manifolds. Given a finite set of sufficiently large positive integers, say J, we construct examples of…

We propose Asymptotic Expansion Conjectures of the relative Reshetikhin-Turaev invariants, of the relative Turaev-Viro invariants and of the discrete Fourier transforms of the quantum 6j-symbols, and prove them for families of special…

We extend Turaev's definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that…