In this work, we compute the representation of the mapping class group of the sphere with 4 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.

中文翻译：

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具有四个穿刺的球体的非半简单 TQFT

在这项工作中，我们计算球体的映射类组的表示4由非半简单 TQFT [C. Blanchet、F. Costantino、N. Geer 和 B. Patureau，非半简单 TQFT、Reidemeister 扭转和 Kashaev 不变量，进阶。数学。 301(2016) 1-78]。我们表明它是忠实的。最后，我们将一般穿孔球体的量子表示与编织组的量子表示进行比较。