Results 1 to 10 of about 1,460 (82)

A relative version of the Turaev–Viro invariants and the volume of hyperbolic polyhedral 3‐manifolds

Journal of Topology, Volume 16, Issue 2, Page 650-678, June 2023., 2023
Abstract We define a relative version of the Turaev–Viro invariants for an ideally triangulated compact 3‐manifold with nonempty boundary and a coloring on the edges, generalizing the Turaev–Viro invariants [36] of the manifold. We also propose the volume conjecture for these invariants whose asymptotic behavior is related to the volume of the manifold
Tian Yang
wiley   +3 more sources

Microscopic description of 2d topological phases, duality and 3d state sums

Advances in Mathematical Physics, Volume 2010, Issue 1, 2010., 2009
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.
Kadar, Zoltan, Marzuoli, Annalisa, Rasetti, Mario   +2 more
core   +3 more sources

Asymptotic additivity of the Turaev–Viro invariants for a family of 3‐manifolds

Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3043-3068, December 2022., 2022
Abstract In this paper, we show that the Turaev–Viro invariant volume conjecture posed by Chen and Yang is preserved under gluings of toroidal boundary components for a family of 3‐manifolds. In particular, we show that the asymptotics of the Turaev–Viro invariants are additive under certain gluings of elementary pieces arising from a construction of ...
Sanjay Kumar, Joseph M. Melby
wiley   +1 more source

Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation [PDF]

, 2010
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting.
Ben W. Reichardt, D. Aharonov, Gorjan Alagic, M. Nielsen, P. Wocjan, Robert König, S. Garnerone, Stephen P. Jordan, T. Kohno, U. Pachner, V. G. Turaev, V. Turaev   +11 more
core   +2 more sources

Holonomy observables in Ponzano-Regge type state sum models [PDF]

, 2011
We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contrast them to the well studied observables on the spin labels.
Barrett J W, Barrett J W, Barrett J W, Bonzom V Smerlak M, Bonzom V Smerlak M, Crane L Yetter D N, Dubois J, Frank Hellmann, Freidel L, Freidel L, John W Barrett, Karowski M, Majid S, Ponzano G, Yetter D N   +14 more
core   +2 more sources

On the relation between two quantum group invariants of 3-cobordisms [PDF]

, 1995
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 ...
Beliakova, A, Durhuus, B
core   +2 more sources

Exact Computations in Topological Abelian Chern‐Simons and BF Theories

Advances in High Energy Physics, Volume 2017, Issue 1, 2017., 2017
We introduce Deligne cohomology that classifies U(1) fibre bundles over 3 manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in U(1) Chern‐Simons theory (BF theory, resp.) at the level of functional integrals. The partition functions (and observables)
Philippe Mathieu, Ralf Hofmann
wiley   +1 more source

Quantum invariants of periodic three-manifolds [PDF]

, 1999
Let p be an odd prime and r be relatively prime to p. Let G be a finite p-group. Suppose an oriented 3-manifold M-tilde has a free G-action with orbit space M. We consider certain Witten-Reshetikhin-Turaev SU(2) invariants w_r(M).
Gilmer, Patrick M.
core   +3 more sources

Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity [PDF]

, 2011
In this work we investigate the canonical quantization of 2+1 gravity with cosmological constant $\Lambda>0$ in the canonical framework of loop quantum gravity.
A Alekseev, A Ashtekar, A Ashtekar, A Ashtekar, A Ashtekar, A Corichi, A Perez, A Perez, A. Perez, AY Alekseev, AY Alekseev, C Meusburger, C Rovelli, C Rovelli, D Oriti, D. Pranzetti, E Alesci, E Alesci, E Buffenoir, E Witten, E Witten, E Witten, H Sahlmann, J Lewandowski, JC Baez, JC Baez, JC Baez, K Noui, K. Noui, L Freidel, LH Kauffman, LH Kauffmann, M Duflo, M Han, N Reshetikhin, S Mizoguchi, T Jacobson, V Bonzom, V Bonzom, VG Turaev, VV Fock   +40 more
core   +4 more sources

Spin Foam Diagrammatics and Topological Invariance [PDF]

, 2001
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF ...
Alejandro Perez, Baez J C, Barrett J W, Florian Girelli, Freidel L, Freidel L, Markopoulou F, Massey W S, Oeckl R, Oeckl R, Pachner U, Perez A, Ponzano G, Reisenberger M, Reisenberger M, Reshetikhin N Yu, Robert Oeckl, Rourke C, Turaev V G, Zapata J A   +19 more
core   +2 more sources