Any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image.
@cite_10: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite-dimensional extension of the quantum group is presented.
Bantay also calculated the images of certain representations of mapping class groups on the Hilbert space of an orbifold model associated to @math @cite_10 . These representations appear to coincide with the twisted Dijkgraaf-Witten representations. However, due to lack of proof, the precise connection is unclear.