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Pré-Publication, Document De Travail Année : 2024

Hennings TQFTs for Cobordisms Decorated With Cohomology Classes

Bangxin Wang
  • Fonction : Auteur

Résumé

Starting from an abelian group $G$ and a factorizable ribbon Hopf $G$-bialgebra $H$, we construct a TQFT $J_H$ for connected framed cobordisms between connected surfaces with connected boundary decorated with cohomology classes with coefficients in $G$. When restricted to the subcategory of cobordisms with trivial decorations, our functor recovers a special case of Kerler-Lyubashenko TQFTs, namely those associated with factorizable ribbon Hopf algebras. Our result is inspired by the work of Blanchet-Costantino-Geer-Patureau, who constructed non-semisimple TQFTs for admissible decorated cobordisms using the unrolled quantum group of $\mathfrak{sl}_2$, and by that of Geer-Ha-Patureau, who reformulated the underlying invariants of admissible decorated $3$-manifolds using ribbon Hopf $G$-coalgebras. Our work represents the first step towards a homological model for non-semisimple TQFTs decorated with cohomology classes that appears in a conjecture by the first two authors.

Dates et versions

hal-04504365 , version 1 (14-03-2024)

Identifiants

Citer

Marco de Renzi, Jules Martel, Bangxin Wang. Hennings TQFTs for Cobordisms Decorated With Cohomology Classes. 2024. ⟨hal-04504365⟩
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