Given the existence of a non-zero degree map between spaces satisfying rational Poincaré duality, does it follow that the target is formal if the domain is formal (in the rational homotopy theoretic sense)? I will discuss some results pointing towards a potential positive answer, both in the topological and holomorphic settings, where in the latter Serre duality plays the role of Poincaré duality and there are several contenders for a correct notion of formality.

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