Results 11 to 20 of about 357 (103)
Abelian BF theory and Turaev-Viro invariant [PDF]
Journal of Mathematical Physics, 2016 The U(1) BF quantum field theory is revisited in the light of Deligne-Beilinson cohomology. We show how the U(1) Chern-Simons partition function is related to the BF one and how the latter on its turn coincides with an abelian Turaev-Viro invariant. Significant differences compared to the non-abelian case are highlighted.
P. Mathieu, F. Thuillier
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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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The Turaev-viro Invariant for 3-Manifolds is a Sum of Three Invariants
Canadian Mathematical Bulletin, 1996 AbstractWe show that every Turaev-Viro invariant for 3-manifolds is a sum of three new invariants and discuss their properties. We also find a solution of a conjecture of L. H. Kauffman and S. Lins. Tables of the invariants for closed orientable 3-manifolds of complexity ≤ 3 are presented at the end of the paper.
M. V. Sokolov
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The invariant of Turaev-Viro from Group category
, 2006 24p ref ...
Petit, Jerome
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Algorithms and Complexity for Turaev-Viro Invariants [PDF]
Journal of Applied and Computational Topology, 2015 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 of complexity for $r=3$ and $r=4$,
Benjamin A. Burton +2 more
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Kuperberg and Turaev–Viro invariants in unimodular categories [PDF]
Pacific Journal of Mathematics, 2020 30 pages, 24 ...
Costantino, Francesco +3 more
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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.
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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
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Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit [PDF]
, 2011 The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit ...
Gorjan Alagic +3 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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