Related papers: Quantum invariants of Seifert 3-manifolds and thei…

We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra $\mathfrak g$ in terms of the Seifert invariants and standard data for…

We formulate the Asymptotic Expansion Conjecture for the Witten-Reshetikhin-Turaev quantum invariants of closed oriented three manifolds. For finite order mapping tori, we study these quantum invariants via the geometric gauge theory…

We calculate the large quantum level asymptotic expansion of the RT-invariants associated to SU(2) of all oriented Seifert 3-manifolds X with orientable base or non-orientable base with even genus. Moreover, we identify the Chern-Simons…

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…

In this article, we obtain an asymptotic expansion formula for the relative Reshetikhin-Turaev invariant in the case that the ambient 3-manifold is gained by doing rational surgery along one component of Whitehead link. In addition, we…

By methods similar to those used by Lisa Jeffrey, we compute the quantum $\mathrm{SU}(N)$-invariants for mapping tori of trace $2$ homeomorphisms of a genus $1$ surface when $N = 2,3$ and discuss their asymptotics. In particular, we obtain…

This is the third article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this paper, by using the saddle point method developed by Ohtsuki and Yokota, we obtain an…

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 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 give a new proof of Witten asymptotic conjecture for Seifert manifolds with non vanishing Euler class and one exceptional fiber. Our method is based on semiclassical analysis on a two dimensional phase space torus. We prove that the…

We study the asymptotic behavior of the Witten-Reshetikhin-Turaev invariant associated with the square of the $n$-th root of unity with odd $n$ for a Seifert fibered space obtained by an integral Dehn surgery along a torus knot. We show…

We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and 3--manifolds, de…

In this paper we construct invariants of 3-manifolds "\`a la Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories which lead to a family of 3-manifold invariants…

This survey covers some of the results contained in the papers by Costantino, Geer and Patureau (https://arxiv.org/abs/1202.3553) and by Blanchet, Costantino, Geer and Patureau (https://arxiv.org/abs/1404.7289). In the first one the authors…

We investigate the Reshetikhin--Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double…

We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition function at or around roots of unity $q=e^{2\pi i \frac{1}{K}}$ with rational level $K=\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the exact…

We state Asymptotic Expansion and Growth Rate conjectures for the Witten-Reshetikhin-Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order…

We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds and establishing quantum modularity of false theta…

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular…

In this paper we engage in a general study of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants of mapping tori of surface mapping class group elements. We use the geometric construction of the Witten-Reshetikhin-Turaev…