Results 21 to 30 of about 1,460 (82)
Turaev–Viro invariants and cabling operations
International Journal of Mathematics, 2023 In this paper, we study the variation of the Turaev–Viro invariants for [Formula: see text]-manifolds with toroidal boundary under the operation of attaching a [Formula: see text]-cable space. We apply our results to a conjecture of Chen and Yang which relates the asymptotics of the Turaev–Viro invariants to the simplicial volume of a compact oriented
Kumar, Sanjay, Melby, Joseph M.
openaire +2 more sources
Turaev–Viro invariants, colored Jones polynomials, and volume [PDF]
Quantum Topology, 2018 We obtain a formula for the Turaev–Viro invariants of a link complement in terms of values of the colored Jones polynomials of the link. As an application, we give the first examples of 3-manifolds where the “large r ” asymptotics of the Turaev–Viro invariants determine the hyperbolic ...
Renaud Detcherry +2 more
openaire +3 more sources
Modified Turaev-Viro invariants from quantum \(\mathfrak{sl}(2|1)\) [PDF]
Journal of Knot Theory and Its Ramifications, 2020 The main result of this paper is that the category of finite-dimensional modules over \(U_q(\mathfrak{sl}(2|1))\) can be converted, in a systematic way, into a ``relative \(G\)-spherical category'', where \(G = \mathbb{C}/\mathbb{Z}\). The usual construction of spherical fusion categories from quantum groups involves specializing \(q\) to a root of ...
Anghel, Cristina Ana-Maria, Geer, Nathan
openaire +3 more sources
Turaev–Viro invariant and 3nj symbols [PDF]
Journal of Mathematical Physics, 2000 We propose in this work a new method to construct the Turaev–Viro state sums, using a diagrammatic presentation describing surgery operation as Heegaard splittings. The resulting invariants can be connected with suitable 3nj symbols, and we evaluate them for the lens spaces.
openaire +2 more sources
Growth of Turaev–Viro invariants and cabling [PDF]
Journal of Knot Theory and Its Ramifications, 2019 The Chen–Yang volume conjecture [Q. Chen and T. Yang, Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants, preprint (2015), arXiv:1503.02547] states that the growth rate of the Turaev–Viro invariants of a compact oriented [Formula: see text]-manifold determines its simplicial volume.
openaire +3 more sources
3-Dimensional Gravity and the Turaev-Viro Invariant [PDF]
Progress of Theoretical Physics Supplement, 1992 We derived an asymptotic formula for q-6j symbol. This is a generalization of the former work by Ponzano and Regge. Studying the q-deformed su(2) spin network as a 3-dimensional quantum gravity model, we show that the Turaev-Viro invariant defines naturally regularized path-integral a la Ponzano-Regge in the semi-classical continuum limit.
Shun'ya Mizoguchi, Tsukasa Tada
openaire +1 more source
2D Conformal Field Theories and Holography [PDF]
, 2002 It is known that the chiral part of any 2d conformal field theory defines a 3d topological quantum field theory: quantum states of this TQFT are the CFT conformal blocks.
Alekseev A. Yu. +19 more
core +2 more sources
Quantum Deformation of Lattice Gauge Theory [PDF]
, 1996 A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex.
Boulatov, D. V.
core +3 more sources
On the Turaev-Viro endomorphism, and the colored Jones polynomial
, 2012 By applying a variant of the TQFT constructed by Blanchet, Habegger, Masbaum, and Vogel, and using a construction of Ohtsuki, we define a module endomorphism for each knot K by using a tangle obtained from a surgery presentation of K.
Cai, Xuanting, Gilmer, Patrick M.
core +1 more source
Observables in 3-dimensional quantum gravity and topological invariants
, 2004 In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model.
Barrett J W +10 more
core +1 more source