Fusion 2-categories and a state-sum invariant for 4-manifolds

2018/12/31 by Christopher L. Douglas, Douglas, Christopher L., David Reutter +1 · 17 citations
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1812.11933

openalex publication_date 2018/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.

Cited by

• Global symmetries: locality, unitarity, and regularity
• Geometric Categories for Continuous Gauging
• The braided monoidal structure of tube algebra representations
• Generalized Witt and Morita equivalences
• How to Build Anomalous (3+1)d Topological Quantum Field Theories
• Secret communication games and a hierarchy of quasiparticle statistics in 3 + 1D topological phases
• The Classification of 3+1d Symmetry Enriched Topological Order
• Finite semisimple module 2-categories
• Non-invertible topological defects in 4-dimensional ℤ₂ pure lattice gauge theory
• Finite 2-group gauge theory and its 3+1D lattice realization
• Higher Idempotent Completion for Soergel Bimodules
• Categorical Anomaly Matching
• Q-system completion is a 3-functor
• Mutual Influence of Symmetries and Topological Field Theories
• The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs
• Large condensation in enriched ∞-categories
• The 2-Category of Topological Quantum Computation

Related

• Finite groups, spherical 2-categories, and 4-manifold invariants
• State-Sum Invariants of 4-Manifolds I
• Categorical 4-manifold invariants from trisection diagrams
• On two approaches to 3-dimensional TQFTs
• Evaluating TQFT invariants from G-crossed braided spherical fusion categories via Kirby diagrams with 3-handles