Renormalized Hennings Invariants and 2+1-TQFTs

Understand

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.