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In this work, we compute the representation of the mapping class group of thesphere with $4$ punctures arising from the non semi-simple TQFT (constructed byBlanchet--Costantino--Geer--Patureau). We show that it is faithful. Lastly, wecompare quantum representations of punctured spheres in general with those ofbraid groups.

The non semi-simple TQFT of the sphere with four punctures