Cochain valued TQFTs from nonsemisimple modular tensor categoriesConfirmed

by Agustina Czenky (University of Southern California)

Friday Jan 9, 2026, 2:30 PM → 4:00 PM America/Toronto

PI/3-394 - Skyroom (Perimeter Institute for Theoretical Physics)

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.