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Renormalized Hennings Invariants and 2 + 1-TQFTs

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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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Authors and Affiliations

  1. Université Paris Diderot - Paris 7, Sorbonne Paris Cité, IMJ-PRG, UMR 7586 CNRS, 75013, Paris, France

    Marco De Renzi

  2. Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA

    Nathan Geer

  3. Univ. Bretagne - Sud, UMR 6205, LMBA, 56000, Vannes, France

    Bertrand Patureau-Mirand

Authors
  1. Marco De Renzi
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  2. Nathan Geer
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  3. Bertrand Patureau-Mirand
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Correspondence to Nathan Geer.

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Communicated by C. Schweigert

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De Renzi, M., Geer, N. & Patureau-Mirand, B. Renormalized Hennings Invariants and 2 + 1-TQFTs. Commun. Math. Phys. 362, 855–907 (2018). https://doi.org/10.1007/s00220-018-3187-8

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