Results 41 to 50 of about 1,460 (82)

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   +2 more sources

Triangulations of 3-dimensional pseudomanifolds with an application to state-sum invariants

, 2004
We demonstrate the triangulability of compact 3-dimensional topological pseudomanifolds and study the properties of such triangulations, including the Hauptvermutung and relations by Alexander star moves and Pachner bistellar moves.
Carter, Greg Friedman, Hudson, Kauffman, Markus Banagl, Rourke, Turaev   +6 more
core   +1 more source

Bicategories for boundary conditions and for surface defects in 3-d TFT

, 2013
We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that
A. Joyal, A. Kapustin, A. Kitaev, A.A. Davydov, A.A. Davydov, A.A. Kirillov, A.D. Lauda, Alessandro Valentino, B. Pareigis, Christoph Schweigert, E. Witt, G. Delfino, G. Moore, G. Moore, G.M.T. Watts, J. Fröhlich, J. Fröhlich, J. Fuchs, J. Fuchs, J. Fuchs, J. Greenough, Jürgen Fuchs, M. Khovanov, M. Müger, M. Müger, N.Yu. Reshetikhin, P. Bowcock, P. Schauenburg, P.I. Etingof, P.I. Etingof, R. Bezrukavnikov, S. Beigi, V. Ostrik, V.B. Petkova, V.G. Drinfeld, V.G. Drinfeld   +35 more
core   +1 more source

Quantum Tetrahedra

, 2009
We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing.
Carfora, Mauro, Marzuoli, Annalisa, Rasetti, Mario   +2 more
core   +1 more source

Topological Invariants For Lens Spaces And Exceptional Quantum Groups

, 1996
The Reshetikhin - Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras $G_2$, $F_4$ and $E_8$ at odd roots of unity are constructed and explicitly computed for all the lens spaces.Comment: LaTeX 10 ...
Zhang, R. B.
core   +2 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, Kalfagianni, Efstratia   +1 more
openaire   +3 more sources

On 3-dimensional Homotopy Quantum Field Theory, I

, 2012
Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane space K(G,1)
Turaev, Vladimir, Virelizier, Alexis
core   +2 more sources

3-dimensional Gravity from the Turaev-Viro Invariant

, 1991
We study the $q$-deformed su(2) spin network as a 3-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines naturally regularized path-integral $\grave{\rm a}$ la Ponzano-Regge, In which a contribution from the cosmological term is effectively included.
Mizoguchi, Shun'ya, Tada, Tsukasa
openaire   +2 more sources

Turaev-Viro invariants as an extended TQFT II

, 2010
In this paper, we present the next step in the proof that $Z_{TV,\C} = Z_{RT, Z(\C)}$, namely that the theories give the same 3-manifold invariants. In future papers we will show that this equality extends to an equivalence of TQFTs.
openaire   +3 more sources

Periods, the meromorphic 3D-index and the Turaev-Viro invariant

Communications in Number Theory and Physics
The 3D-index of Dimofte-Gaiotto-Gukov is an interesting collection of $q$-series with integer coefficients parametrised by a pair of integers and associated to a 3-manifold with torus boundary. In this note, we explain the structure of the asymptotic expansions of the 3D-index when $q=e^{2πiτ}$ and $τ$ tends to zero (to all orders and with ...
Garoufalidis, Stavros, Wheeler, Campbell
openaire   +2 more sources