Non-semi-simple TQFT of the sphere with four punctures

Abstract

In this work, we compute the representation of the mapping class group of the sphere with [Formula: see text] punctures arising from the non-semi-simple TQFT [C. Blanchet, F. Costantino, N. Geer and B. Patureau, Non-semi-simple TQFTs, Reidemeister torsion and Kashaev’s invariants, Adv. Math. 301 (2016) 1–78]. We show that it is faithful. Lastly, we compare quantum representations of punctured spheres in general with those of braid groups.