Alterfold TQFT gives a unified topological proof framework for modular invariants, alpha-induction, and flat connections, plus new higher-genus and multi-context invariants.
On a necessary condition for unitary categorification of fusion rings
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abstract
In arXiv:1910.12059 Liu, Palcoux and Wu proved a remarkable necessary condition for a fusion ring to admit a unitary categorification, by constructing invariants of the fusion ring that have to be positive if it is unitarily categorifiable. The main goal of this note is to provide a somewhat more direct proof of this result. In the last subsection we discuss integrality properties of the Liu-Palcoux-Wu invariants.
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Alterfold Theory and Topological Modular Invariance
Alterfold TQFT gives a unified topological proof framework for modular invariants, alpha-induction, and flat connections, plus new higher-genus and multi-context invariants.