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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.
Tsukasa Tada
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On Hempel Pairs and Turaev-Viro Invariants
Chinese Annals of Mathematics Series B22 pages; calculation corrected; Remark 4.2 ...
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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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3-Dimensional Gravity and the Turaev-Viro Invariant [PDF]
Progress of Theoretical Physics Supplement, 1992 We derived an asymptotic formula for q-6j symbol. This is a generalization of the former work by Ponzano and Regge. Studying the q-deformed su(2) spin network as a 3-dimensional quantum gravity model, we show that the Turaev-Viro invariant defines naturally regularized path-integral a la Ponzano-Regge in the semi-classical continuum limit.
Tsukasa Tada
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On a simple invariant of Turaev-Viro type
Journal of Mathematical Sciences, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matveev, S. V., Sokolov, M. V.
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2003
These invariants were first described by V. Turaev and 0. Viro [121]. They possess two important properties. First, just like homology groups, they are easy to calculate. Only the limitations of the computer at hand may cause some difficulties. Second, they are very powerful, especially if used together with the first homology group.
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These invariants were first described by V. Turaev and 0. Viro [121]. They possess two important properties. First, just like homology groups, they are easy to calculate. Only the limitations of the computer at hand may cause some difficulties. Second, they are very powerful, especially if used together with the first homology group.
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GRAPHICAL APPROACH TO THE 3-MANIFOLD INVARIANTS OF TURAEV-VIRO
Journal of Knot Theory and Its Ramifications, 1992This paper uses graphical techniques introduced by Kirillov and Reshetikhin to give an alternative approach to the construction of the Turaev-Viro invariants for links in \(S^ 3 \) and for closed 3- manifolds. The invariant is defined in terms of a regular diagram for the link (or for a framed link representing the manifold) and is shown to be ...
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Which lens spaces are distinguished by Turaev-Viro invariants
Mathematical Notes, 1997Using the works of \textit{S. Yamada} [J. Knot Theory Ramifications 4, No. 2, 319-327 (1995; Zbl 0843.57004)] and \textit{L. C. Jeffrey} [Commun. Math. Phys. 147, No. 3, 563-604 (1992; Zbl 0755.53054)], the author gives an explicit formula for the value of the Turaev-Viro invariants of the 3-dimensional lens spaces \(L_{p,q}\).
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Possible universal quantum algorithms for generalized Turaev-Viro invariants
Proceedings of SPIE, 2011An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for ...
Mario Velez, Juan Ospina
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