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Tensor categories and alterfold theory

组织者

Vassily Manturov , 任世全 , 万喆彦

演讲者

明爽

时间

2024年08月07日 15:30 至 17:00

地点

A3-2-301

线上

Zoom 831 5020 0580 (141592)

摘要

In this talk, I will introduce a partition function defined on bi-colored three-manifolds decorated by tensor diagrams from a spherical fusion category \mathcal{C}. We called them 3 dimensional alterfold. This partition function yields three-manifold invariants and three-dimensional topological quantum field theories (TQFTs). I will discuss how well-known invariants and TQFTs, such as Turaev-Viro theory and Reshetikhin-Turaev theory, can be naturally embedded within our framework. Furthermore, our bi-colored theory provides topological interpretations for fundamental concepts in tensor categories, including the Drinfeld center and Frobenius-Schur indicators. We expect the theory could generalizes to higher dimensions, and could produce new identities for (higher) tensor categories.