Résumé
Comm. Math. Phys. 362 (2018), no. 3, 855-907 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.