On 3-dimensional homotopy quantum field theory III: Comparison of two approaches

DOI10.1142/S0129167X20500767zbMath1473.57032arXiv1911.10257MaRDI QIDQ5130973

Alexis Virelizier, Vladimir G. Turaev

Publication date: 31 October 2020

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.10257

zbMATH Keywords

Turaev-Viro invariantsstate sum invariantsHQFTsurgery invariantsgraded fusion categories

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56) Symmetric monoidal categories (19D23) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16)

Related Items (14)

Holonomy invariants of links and nonabelian Reidemeister torsion ⋮ Module Eilenberg-Watts calculus ⋮ Bicategories for boundary conditions and for surface defects in 3-d TFT ⋮ Hopf polyads ⋮ Equivariant Morita theory for graded tensor categories ⋮ Asymptotic density of states in 2d CFTs with non-invertible symmetries ⋮ Monoidal categories graded by crossed modules and 3-dimensional HQFTs ⋮ State sum invariants of three manifolds from spherical multi-fusion categories ⋮ Invertible bimodule categories and generalized Schur orthogonality ⋮ A \(G\)-equivariant string-net construction ⋮ The moonshine anomaly ⋮ CFT correlators for Cardy bulk fields via string-net models ⋮ Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies ⋮ Extended TQFTs via generators and relations I: The extended toric code

Cites Work

• Unnamed Item
• On the graded center of graded categories
• Centers of graded fusion categories
• Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier.
• Extended homotopy quantum field theories and their orbifoldization
• Monoidal categories and topological field theory
• ON 3-DIMENSIONAL HOMOTOPY QUANTUM FIELD THEORY, I
• Tensor Categories
• On 3-dimensional homotopy quantum field theory II: The surgery approach
• Quantum invariants of knots and 3-manifolds

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