Results 11 to 20 of about 459 (91)
Asymptotic additivity of the Turaev–Viro invariants for a family of 3‐manifolds
Journal of the London Mathematical Society, 2022 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 Turaev-Viro invariants are additive under certain gluings of elementary pieces arising from a construction of ...
Kumar, Sanjay, Melby, Joseph M.
openaire +3 more sources
Gromov norm and Turaev-Viro invariants of 3-manifolds
Annales scientifiques de l'École normale supérieure, 2020 28 pages, no figures: Miinor revisions. Ann. Sci. Ecole Norm.
Detcherry, Renaud +1 more
openaire +4 more sources
A manifestly Morita-invariant construction of Turaev–Viro invariants
Quantum TopologyWe present a state sum construction that assigns a scalar to a skeleton in a closed oriented three-dimensional manifold. The input datum is the pivotal bicategory \mathbf{Mod}^{\mathrm{sph}}(\mathcal{A}) of spherical module categories over a ...
Jürgen Fuchs +3 more
openaire +3 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
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
Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants [PDF]
Quantum Topology, 2018 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}) .
Chen, Qingtao, Yang, Tian
openaire +3 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
Three-dimensional gravity from the Turaev-Viro invariant [PDF]
Physical Review Letters, 1992 Summary: We study the \(q\)-deformed su(2) spin network as a three-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines a naturally regularized path integral a la Ponzano and Regge, in which a contribution from the cosmological term is effectively included.
Mizoguchi, Shun'ya, Tada, Tsukasa
openaire +2 more sources
Exact Computations in Topological Abelian Chern‐Simons and BF Theories
Advances in High Energy Physics, Volume 2017, Issue 1, 2017., 2017 We introduce Deligne cohomology that classifies U(1) fibre bundles over 3 manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in U(1) Chern‐Simons theory (BF theory, resp.) at the level of functional integrals. The partition functions (and observables)
Philippe Mathieu, Ralf Hofmann
wiley +1 more source
Asymptotics of the Turaev-Viro invariants and their connections in low-dimensional topology
, 2021 We study the Turaev-Viro invariants of 3-manifolds as well as their relationship to invariants arising from hyperbolic geometry. We first construct a closed formula for the Turaev-Viro invariants for hyperbolic once-punctured torus bundles.
Kumar, Sanjay Lakshman
core +1 more source