Results 31 to 40 of about 1,522 (82)
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
Asymptotics of quantum 6j$6j$‐symbols and generalized hyperbolic tetrahedra
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract We establish the geometry behind the quantum 6j$6j$‐symbols under only the admissibility conditions as in the definition of the Turaev–Viro invariants of 3‐manifolds. As a classification, we show that the 6‐tuples in the quantum 6j$6j$‐symbols give in a precise way to the dihedral angles of (1) a spherical tetrahedron, (2) a generalized ...
Giulio Belletti, Tian Yang
wiley +1 more source
Computing Turaev-Viro invariants for 3-manifolds
Manuscripta Mathematica, 1991 This note outlines a scheme to compute the Turaev-Viro invariants of a closed 3-manifold, and tabulates the values of the invariant corresponding to certain 8th roots of unity for a number of manifolds.
Kauffman, Lous H., Lins, Sóstences
openaire +2 more sources
(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces
, 2017 We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects.
Dittrich, Bianca
core +1 more source
Colored Turaev–Viro invariants of twist knots
Topology and its Applications, 2009 This paper presents formulae for the colored Turaev-Viro invariants [introduced by \textit{J. Barrett, J. Martins} and \textit{J. García-Islas}, J. Math. Phys. 48, No.~9, 093508, 18~p. (2007; Zbl 1152.81328)] of twist knots. These formulae are obtained by a fairly lengthy computation which uses the description of the colored Turaev-Viro invariants as a
openaire +1 more source
Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot
, 2020 In this paper we investigate the asymptotic behavior of the colored Jones polynomials and the Turaev-Viro invariants for the figure eight knot. More precisely, we consider the $M$-th colored Jones polynomials evaluated at $(N+1/2)$-th root of unity with ...
Au, Thomas Kwok-Keung, Wong, Ka Ho
core
Braiding and entanglement in spin networks: a combinatorial approach to topological phases
, 2008 The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding.
Kadar, Zoltan +2 more
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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
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Turaev-Viro invariants as an extended TQFT
, 2010 38 pages, many figures. New in v.3: significantly rewritten exposition, providing details of some proofs which were only outlined in the previous ...
Kirillov Jr., Alexander +1 more
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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
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