Finiteness of Mapping Class Group Representations from Twisted Dijkgraaf-Witten Theory

Understand

We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image.

• This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images are finite.
• In particular, our result answers their question regarding finiteness of images of arbitrary mapping class group representations in the affirmative.
• Our approach is to translate the problem into manipulation of colored graphs embedded in the given surface.