Renormalized Hennings Invariants and 2+1-TQFTs

Abstract

We construct non-semisimple $2+1$-TQFTs yielding mapping class group representations in Lyubashenko's spaces. In order to do this, we first generalize Beliakova, Blanchet and Geer's logarithmic Hennings invariants based on quantum ${\mathfrak{sl}}_2$ to the setting of finite-dimensional non-degenerate unimodular ribbon Hopf algebras. The tools used for this construction are a Hennings-augmented Reshetikhin-Turaev functor and modified traces. When the Hopf algebra is factorizable, we further show that the universal construction of Blanchet, Habegger, Masbaum and Vogel produces a $2+1$-TQFT on a not completely rigid monoidal subcategory of cobordisms.

References in corpus (1)

• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models

Cited by in corpus (10)

• 3-Dimensional TQFTs From Non-Semisimple Modular Categories
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• On dualizability of braided tensor categories
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• Logarithmic Hennings invariants for restricted quantum sl(2)
• Non-Semisimple Extended Topological Quantum Field Theories
• Modified traces for quasi-Hopf algebras
• Kuperberg and Turaev-Viro Invariants in Unimodular Categories
• Monadic cointegrals and applications to quasi-Hopf algebras
• Diagrammatic Construction of Representations of Small Quantum ${\mathfrak{sl}}_2$