Non-compact 3D TQFT and Non-semisimple Modular Tensor Categories
Published:Dec 29, 2025 18:55
•1 min read
•ArXiv
Analysis
This paper explores a non-compact 3D Topological Quantum Field Theory (TQFT) constructed from potentially non-semisimple modular tensor categories. It connects this TQFT to existing work by Lyubashenko and De Renzi et al., demonstrating duality with their projective mapping class group representations. The paper also provides a method for decomposing 3-manifolds and computes the TQFT's value, showing its relation to Lyubashenko's 3-manifold invariants and the modified trace.
Key Takeaways
Reference
“The paper defines a non-compact 3-dimensional TQFT from the data of a (potentially) non-semisimple modular tensor category.”