On invariants of modular categories beyond modular data


We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the W-matrix—the quantum invariant of a colored framed Whitehead link from the associated TQFT of a modular category. We prove that the W-matrix and the set of punctured S-matrices are strictly beyond the modular data . Whether or not the triple constitutes a complete invariant of modular categories remains an open question.

J. Pure Appl. Algebra 223 (2019), no. 9, 4065–4088.