Tensor categories and alterfold theory
Organizers
Vassily Manturov
, Shiquan Ren
,
Zhe Yan Wan
Speaker
Time
Wednesday, August 7, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580
(141592)
Abstract
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.