Results 31 to 40 of about 459 (91)
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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Computations of Turaev-Viro-Ocneanu Invariants of 3-Manifolds from Subfactors [PDF]
Journal of Knot Theory and Its Ramifications, 2003 In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjugate linear isomorphism preserving ...
Sato, Nobuya, Wakui, Michihisa
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Computation of Large Asymptotics of 3-Manifold Quantum Invariants
, 2021 International audienceQuantum topological invariants have played an important role in computational topology, and they are at the heart of major modern mathematical conjectures.
Rouillé, Owen +3 more
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Periods, the meromorphic 3D-index and the Turaev-Viro invariant
Communications in Number Theory and PhysicsThe 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
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On the relation between two quantum group invariants of 3-cobordisms [PDF]
, 1996 We prove in the context of quantum groups at even roots of unity that a Turaev-Viro type invariant of a three-dimensional cobordism M equals the tensor product of the Reshetikhin-Turaev invariants of M and M*, where the latter denotes M with orientation ...
Durhuus, B, Beliakova, A
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Asymptotics of the Relative Reshetikhin-Turaev Invariants [PDF]
, 2023 In this dissertation, we study the asymptotic expansion conjecture of the relative Reshetikhin-Turaev invariants proposed by T. Yang and the author in [65] for all pairs (M, L) satisfying the property that M L is homeomorphic to some fundamental shadow
Wong, Ka Ho
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Admissible colourings of 3-manifold triangulations for Turaev-Viro type invariants
CoRR, 2015 Turaev Viro invariants are amongst the most powerful tools to distinguish 3-manifolds: They are implemented in mathematical software, and allow practical computations. The invariants can be computed purely combinatorially by enumerating colourings on the edges of a triangulation T. These edge colourings can be interpreted as embeddings of surfaces in T.
Clément Maria, Jonathan Spreer
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Modified 6j-symbols and 3-manifold invariants
, 2011 We show that the renormalized quantum invariants of links and graphs in the 3-sphere, derived from tensor categories in Geer et al. (2009) [14], lead to modified 6j-symbols and to new state sum 3-manifold invariants.
Turaev, Vladimir +8 more
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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.
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Generalized Abelian Turaev-Viro and $\mathrm{U}\!\left(1\right)$ BF Theories
, 2023 International audienceWe explain how it is possible to study $\mathrm{U}\!\left(1\right)$ BF theory over a connected closed oriented smooth $3$-manifold in the formalism of path integral thanks to Deligne-Beilinson cohomology.
Thuillier, Frank +2 more
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