Results 1 to 10 of about 30 (29)

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

Journal of the London Mathematical Society, 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
exaly   +2 more sources

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   +1 more source

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

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, Annalisa Marzuoli, Mario Rasetti, Debashish Goswami   +3 more
wiley   +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

What Chern-Simons theory assigns to a point. [PDF]

Proc Natl Acad Sci U S A, 2017
Henriques AG.
europepmc   +1 more source

The Spin-Foam Approach to Quantum Gravity. [PDF]

Living Rev Relativ, 2013
Perez A.
europepmc   +1 more source

Higher categories, colimits, and the blob complex. [PDF]

Proc Natl Acad Sci U S A, 2011
Morrison S, Walker K.
europepmc   +1 more source

Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe. [PDF]

Living Rev Relativ, 2005
Carlip S.
europepmc   +1 more source

CFT Correlators and Mapping Class Group Averages. [PDF]

Commun Math Phys
Romaidis I, Runkel I.
europepmc   +1 more source