Non-semisimple link and manifold invariants for symplectic fermions

Abstract: I will talk about link and three-manifold invariants defined in terms of a non-semisimple finite ribbon category C together with a choice of tensor ideal and modified trace. If the ideal is all of C, these invariants agree with those defined by Lyubashenko in the 90’s, and as we show, they only depend on the Grothendieck class of the objects labelling the link. These invariants are therefore not able to determine non-split extensions. However, we observed an interesting phenomenon: if one chooses an intermediate proper ideal between C and the minimal ideal of projective objects, the invariants do distinguish non-trivial extensions. This is demonstrated in the case of C being the ribbon category of N pairs of symplectic fermions. This is a joint work with J. Berger and I. Runkel.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home