Mapping class group representations from Turaev-Viro TQFT for abelian groups

Abstract

It is well known that (2 + 1) topological quantum field theories (TQFTs) induce representations for the mapping class groups (MCGs) of surfaces. In this paper, we work explicitly on the MCG representations of any genus from the Turaev-Viro TQFTs based on the category for the finite abelian group G and cocycle . As an application, we determine for torus the image of the MCG representation with the graphical calculus on the string-net diagram.