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Algorithms and Complexity for Turaev-Viro Invariants [PDF]
Lecture Notes in Computer Science, 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 ...
Francesco Costantino +2 more
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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
Yuya Koda
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On Colored Turaev-Viro Invariants for Links in Arbitrary 3-Manifolds [PDF]
International Mathematics Research Notices, 2009 40 pages, 23 ...
Ekaterina Pervova, Carlo Petronio
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On Hempel Pairs and Turaev-Viro Invariants
Chinese Annals of Mathematics Series B22 pages; calculation corrected; Remark 4.2 ...
Liu, Yi
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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.
openaire +3 more sources
Skein theory and Turaev-Viro invariants
Topology, 1995 Using the so-called chain mail the author identifies two sets of quantum 3-manifold invariants. These were defined by Reshetikin-Turaev respectively Turaev-Viro using different presentations of 3-manifolds and also different quantum initial data. This identification was first done by Walker and Turaev using more complicated methods.
Justin Roberts
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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.
Louis H Kauffman +2 more
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The Turaev-Viro Invariants of All Orientable Closed Seifert Fibered Manifolds
Tokyo Journal of Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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