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Article Dans Une Revue Communications in Mathematical Physics Année : 2018

Renormalized Hennings Invariants and 2+1-TQFTs

Marco de Renzi
Nathan Geer
  • Fonction : Auteur

Résumé

We extend Lyubashenko's non-semisimple modular functors to $2+1$-TQFTs. 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 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. This provides a fully monoidal extension to non-connected surfaces of Kerler's non-semisimple TQFTs for connected surfaces.

Dates et versions

hal-01680395 , version 1 (10-01-2018)

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Citer

Marco de Renzi, Nathan Geer, Bertrand Patureau-Mirand. Renormalized Hennings Invariants and 2+1-TQFTs. Communications in Mathematical Physics, 2018, 362 (3), pp.855-907. ⟨10.1007/s00220-018-3187-8⟩. ⟨hal-01680395⟩

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