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Communications in Mathematical Physics

, Volume 362, Issue 3, pp 855–907 | Cite as

Renormalized Hennings Invariants and 2 + 1-TQFTs

  • Marco De Renzi
  • Nathan Geer
  • Bertrand Patureau-Mirand
Article

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Marco De Renzi
    • 1
  • Nathan Geer
    • 2
  • Bertrand Patureau-Mirand
    • 3
  1. 1.Université Paris Diderot - Paris 7, Sorbonne Paris Cité, IMJ-PRG, UMR 7586 CNRSParisFrance
  2. 2.Mathematics and StatisticsUtah State UniversityLoganUSA
  3. 3.Univ. Bretagne - Sud, UMR 6205, LMBAVannesFrance

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