5 papers
Non-semisimple open-closed 3d TFT
Ingo Runkel, Yilong Wang
Given a spherical finite tensor category C, not necessarily semisimple, and a two-sided modified trace on its projective ideal, we define an open-closed three-dimensional topologic…
Modular fusion categories with trivial Torelli group actions
Liang Chang, Siu-Hung Ng, Yilong Wang
In this paper, we study modular fusion categories whose mapping class group representations are trivial on the Torelli groups, with particular emphasis on the congruence properties…
On the gauge invariance of the Kuperberg invariant of certain high genus framed 3-manifolds
Liang Chang, Yilong Wang, Saifei Zhai
We show that the Kuperberg invariant of the Weeks manifold with any framing is a gauge invariant of finite-dimensional Hopf algebras, which provides the first example of gauge inva…
Generalized Witt and Morita equivalences
Liang Kong, Yilong Wang, Hao Zheng
In this work, we introduce a family of new equivalence relations among fusion categories that are less refined than the usual Morita equivalence. We obtain abelian groups by quotie…
Generalizations of Frobenius-Schur indicators from Kuperberg invariants
Liang Chang, Siu-Hung Ng, Yilong Wang
We introduce an approach to produce gauge invariants of any finite-dimensional Hopf algebras from the Kuperberg invariants of framed 3-manifolds. These invariants are generalizatio…