Results 21 to 30 of about 459 (91)
Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums
Advances in Mathematical Physics, Volume 2010, Issue 1, 2010., 2010 Doubled topological phases introduced by Kitaev, Levin, and Wen supported on two‐dimensional lattices are Hamiltonian versions of three‐dimensional topological quantum field theories described by the Turaev‐Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum.
Zoltán Kádár +3 more
wiley +1 more source
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.
Shun'ya Mizoguchi, Tsukasa Tada
openaire +1 more source
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
openaire +4 more sources
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
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
Admissible Colourings of 3-Manifold Triangulations for Turaev-Viro Type Invariants [PDF]
, 2016 Turaev-Viro invariants are amongst the most powerful tools to distinguish 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them rely on the enumeration of an extremely large set of combinatorial data defined ...
Maria, Clément, Spreer, Jonathan
core +1 more source
Refined invariants and TQFTs from Homfly skein theory [PDF]
, 1999 We work in the reduced SU(N, K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants.
Beliakova, A
core +1 more source
Concordance Invariants and the Turaev Genus
, 2022 We show that the differences between various concordance invariants of knots, including Rasmussen's s-invariant and its generalizations s(n)-invariants, give lower bounds to the Turaev genus of knots.
Sungkyung Kang +2 more
core +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 ...
Wong, Ka Ho, Au, Thomas Kwok-Keung
core +1 more source
The cobordism group of homology cylinders [PDF]
, 2010 Garoufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as an enlargement of the mapping class group.
Friedl, Stefan +5 more
core +1 more source