Renormalized Hennings Invariants and 2+1-TQFTs

Marco De Renzi; Nathan Geer; Bertrand Patureau-Mirand

doi:10.1007/s00220-018-3187-8

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arXiv · 1707.08044

Renormalized Hennings Invariants and 2+1-TQFTs

Marco De Renzi·Nathan Geer·Bertrand Patureau-Mirand

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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.

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Marco De Renzi, Nathan Geer, Bertrand Patureau-Mirand. 2017-07-25. Renormalized Hennings Invariants and 2+1-TQFTs. https://doi.org/10.1007/s00220-018-3187-8

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