We survey earlier results on factorizations of extremal projectors and relative extremal projectors and present preliminary results on non-commutative factorizations of relative extremal projectors: we deduce the existence of such factorizations for sl(4) and sl(5).

This survey focuses on the computational complexity of some of the
fundamental decision problems in 3-manifold theory. The article discusses the
wide variety of tools that are used to tackle these problems, including normal
and almost surfaces, hierarchies, homomorphisms to finite groups, and
hyperbolic structures.

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