3-dimensional TQFTs from non-semisimple modular categories

DOI10.1007/s00029-021-00737-zzbMath1495.57019arXiv1912.02063OpenAlexW2993157255MaRDI QIDQ2071752

Nathan Geer, Ingo Runkel, Azat M. Gainutdinov, Bertrand Patureau-Mirand, Marco De Renzi

Publication date: 31 January 2022

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02063

zbMATH Keywords

TQFTribbon categoryHennings invariantrenormalized Lyubashenko \(3\)-manifold invariantsReshetikhin-Turaev functor

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Fusion categories, modular tensor categories, modular functors (18M20) Braided monoidal categories and ribbon categories (18M15) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

Related Items (9)

Non-semisimple 3-manifold invariants derived from the Kauffman bracket ⋮ Mapping class group representations from non-semisimple TQFTs ⋮ Diagrammatic construction of representations of small quantum \(\mathfrak{sl}_2\) ⋮ On unimodular module categories ⋮ The differential graded Verlinde formula and the Deligne Conjecture ⋮ Constructing non-semisimple modular categories with local modules ⋮ \(\mathrm{SL}_2\) tilting modules in the mixed case ⋮ Monadic cointegrals and applications to quasi-Hopf algebras ⋮ Homotopy coherent mapping class group actions and excision for Hochschild complexes of modular categories

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