String-net model of Turaev-Viro invariants

TL;DR

This paper explores the connection between Turaev-Viro topological quantum field theory and string-net models, especially focusing on surfaces with boundaries, to deepen understanding of their mathematical relationship.

Contribution

It establishes a detailed relation between Turaev-Viro invariants and string-net spaces, extending the analysis to surfaces with boundary.

Findings

Clarified the relation between Turaev-Viro TQFT and string-net models

Extended the analysis to surfaces with boundary

Provided mathematical insights into topological invariants

Abstract

In this paper, we describe the relation between the Turaev--Viro TQFT and the string-net space introduced in the papers of Levin and Wen. In particular, the case of surfaces with boundary is considered in detail.