PIRSA:26010067 Scientific Series Mathematical physics

DOI10.48660/26010067

Series: Mathematical Physics

Czenky, A. (2026). Cochain valued TQFTs from nonsemisimple modular tensor categories. Perimeter Institute. https://pirsa.org/26010067

Czenky, Agustina. Cochain valued TQFTs from nonsemisimple modular tensor categories. Perimeter Institute, Jan. 09, 2026, https://pirsa.org/26010067 

@misc{ pirsa_PIRSA:26010067,
  doi = {10.48660/26010067},
  url = {https://pirsa.org/26010067},
  author = {Czenky, Agustina},
  keywords = {Mathematical physics},
  language = {en},
  title = {Cochain valued TQFTs from nonsemisimple modular tensor categories},
  publisher = {Perimeter Institute},
  year = {2026},
  month = {jan},
  note = {PIRSA:26010067 see, \url{https://pirsa.org}}
}

Abstract

Consider a finite modular tensor category A. In [DGGPR] the authors exhibit a 3-dimensional topological field theory Z_A: Bord(A) -> Vect, which, in the case where A is semisimple, recovers the usual Reshetikhin-Turaev TQFT. In the present work we show that this extends naturally to a TQFT Z_Ch(A), which takes values in the symmetric tensor category Ch(Vect) of linear cochains. This cochain valued theory furthermore respects (certain classes of) homotopies.
 
[DGGPR] M. De Renzi, A. M. Gainutdinov, N. Geer, B. Patureau-Mirand, and I. Runkel. 3-dimensional TQFTs from non-semisimple modular categories. Sel. Math. New Ser., 28(2):42, 2022.

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