arXiv research

We show that for every spherical category $\C$ with invertible dimension, the Turaev-Viro TQFT admits a splitting into blocks which come from an HQFT, called the Turaev-Viro HQFT. The Turaev-Viro HQFT has the classifying space $B\grad$ as target space, where $\grad$ is a group obtained from the category $\C$. This cons…

Paper finds Hempel pairs distinguishable by Turaev-Viro invariants.

The paper finds formulas for a specific invariant order 7.

Turaev-Viro invariants match for certain surface bundles.

Defines a new version of Turaev-Viro invariants for 3-manifolds with boundaries.

Study Turaev-Viro invariants of Seifert fibered 3-manifolds, proving volume conjecture.

The paper proves an asymptotic additivity of Turaev-Viro invariants for a family of 3-manifolds.

Study how Turaev-Viro invariants change with cabling operations.

Paper proves stability of volume conjecture under cabling.

Study Turaev-Viro invariants of 3-manifolds with toroidal boundary.

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), where M is a closed oriented 3-manifold and L is an oriented link in M, by a tria…

Formula connects Turaev-Viro invariants to colored Jones polynomials and hyperbolic volumes.

New construction of Turaev-Viro invariants invariant under Morita equivalence.

We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. Roberts' definition of the Turaev-Viro state sum is exploited. Fu…

In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Tu…

The paper connects Turaev-Viro invariants and Gromov norm of 3-manifolds.

New invariants from quantum group theory for hyperbolic 3-manifolds.

Study on asymptotic behavior of knot invariants for figure eight knot.

The article calculates asymptotic expansions for quantum invariants from surgeries on Whitehead link components.

The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them require exponential time. The invariants are parameterised by an integer $r \geq 3$. We resolve the question …

Turaev Viro invariants are amongst the most powerful tools to distinguish 3-manifolds: They are implemented in mathematical software, and allow practical computations. The invariants can be computed purely combinatorially by enumerating colourings on the edges of a triangulation T. These edge colourings can be interpre…

In this article, we discuss a (2+1)-dimensional topological quantum field theory, for short TQFT, with a Verlinde basis. As a conclusion of this general theory, we have a Dehn surgery formula. We show that Turaev-Viro-Ocneanu TQFT has a Verlinde basis. Several applications of this theorem are exposed. Based on Izumi's …

Paper connects quantum representations to fibered links and Turaev-Viro invariants.

In a previous work arXiv:0903.4512, we have built an homotopical Turaev-Viro invariant and an HQFT from the universal graduation of a spherical category. In the present paper, we show that every graduation $(G,p)$ of a spherical category $\C$ defines an homotopical Turaev-Viro invariant $HTV_{\C}^{(G,p)}$ and an HQFT $…

Categorifies invariants of 3-manifolds using handlebody graphs.

In this paper we show how one can extend Turaev-Viro invariants, defined for an arbitrary spherical fusion category $C$, to 3-manifolds with corners. We demonstrate that this gives an extended TQFT which conjecturally coincides with the Reshetikhin-Turaev TQFT corresponding to the Drinfeld center $Z(C)$. In the present…

Generalizes DW invariants for cusped 3-manifolds, distinguishing some pairs.

In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjuga…

Defines a new 2+1-G-HQFT using graded skein modules.

The 3D-index connects to Turaev-Viro invariant and knot periods.

Researchers compute large quantum invariants for 3-manifolds.

Proves volume conjecture for hyperbolic 3-manifolds using quantum 6j-symbols.

Investigates quantum $6j$ symbols for hyperbolic tetrahedra.

New invariants derived from a modular category for links and 3-manifolds.

The paper proposes and proves asymptotic expansions for quantum invariants.

We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic $3$-manifold, evaluated at the root of unity $\exp({2π\sqrt{-1}}/{r})$ instead of the standard $\exp({π\sqrt{-1}}/{r})$. We present evidence that, as $r$ tends to $\infty$, these invariants grow exponentially with growt…

In this paper, we establish the general theory of (2+1)-dimensional topological quantum field theory (in short, TQFT) with a Verlinde basis. It is a consequence that we have a Dehn surgery formula for 3-manifold invariants for this kind of TQFT's. We will show that Turaev-Viro-Ocneanu unitary TQFT's obtained from subfa…

We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In the case of the three-dimensional invariant, we prove a duality formula relating …

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 Enveloping Algebra of sl(2). This invariant can be considered as a spherical version…

Let C be a spherical fusion category. We prove that the Turaev-Viro-Barrett-Westbury state sum invariant of 3-manifolds derived from C is equal to the Reshetikhin-Turaev surgery invariant of 3-manifolds derived from Z(C), where Z(C) is the Drinfeld-Joyal-Street center of C.

The Chen-Yang volume conjecture is verified for knots in handlebodies with specific boundary components.

Paper uses Turaev-Viro TQFT to estimate 3-manifold genus.

The paper calculates the asymptotics of quantum invariants for Whitehead chains.

The t-invariant can be considered as the Turaev-Viro invariant of order 5 computed for integer colors only. We compute all values of the t-invariant for Seifert manifolds with base sphere and three singular fibers. As a result we show that the manifolds parameters modulo five define the value of the t-invariant. Partia…

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 new state sum 3-manifold invariants. We give examples of categories such that the …

Upper bound conjecture for Yokota invariant proved for polyhedral graphs.

The paper characterizes boundaries in Turaev-Viro TQFTs and Dijkgraaf-Witten theories.

Proves volume conjectures for figure-eight knot surgeries.