2017/02/23 by Shawn X. Cui, Zhenghan Wang · 8 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Categorical variable #Combinatorics #Connected sum #Fusion #Fusion rules #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical physics #Mathematics #Pure mathematics #Simply connected space #Topological quantum field theory #cond-mat.other #math-ph #math.CT #math.GN #math.MP #math.QA #msc:18D10 #msc:57N13 #msc:57R56
paper · pdf · doi:10.1142/s0218216517501048
published in Journal of Knot Theory and Its Ramifications 26(14), 1750104 (World Scientific) · 26 pages, 8 figures
arxiv created 2017/02/23 · openalex publication_date 2017/11/14 · arxiv updated 2017/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We define a family of quantum invariants of closed oriented [Formula: see text]-manifolds using spherical multi-fusion categories (SMFCs). The state sum nature of this invariant leads directly to [Formula: see text]-dimensional topological quantum field theories ([Formula: see text]s), which generalize the Turaev–Viro–Barrett–Westbury ([Formula: see text]) [Formula: see text]s from spherical fusion categories. The invariant is given as a state sum over labeled triangulations, which is mostly parallel to, but richer than the [Formula: see text] approach in that here the labels live not only on [Formula: see text]-simplices but also on [Formula: see text]-simplices. It is shown that a multi-fusion category in general cannot be a spherical fusion category in the usual sense. Thus, we introduce the concept of a SMFC by imposing a weakened version of sphericity. Besides containing the [Formula: see text] theory, our construction also includes the recent higher gauge theory [Formula: see text]-[Formula: see text]s given by Kapustin and Thorngren, which was not known to have a categorical origin before.