Three-dimensional TQFTs via string-nets and two-dimensional surgery [article]

Bruce Bartlett
2022 arXiv   pre-print
If C is a spherical fusion category, the string-net construction associates to each closed oriented surface Σ the vector space Z_SN(Σ) of linear combinations of C-labelled graphs on Σ modulo local relations, in a way which is functorial with respect to orientation-preserving diffeomorphisms of surfaces. We show how to extend this assignment to a 3-dimensional topological quantum field theory (TQFT), by defining how the surgery generators in Juhász' presentation of the oriented 3-dimensional
more » ... ism category act on the string-net vector spaces. We show that the resulting TQFT, which is formulated completely in the two-dimensional graphical language of string-nets, is an alternative description of the Turaev-Viro state sum model.
arXiv:2206.13262v1 fatcat:qnejlt7skbeorgov53oclrqxv4