Poincar\'e dualization and formal domination

Abstract

We consider the question of whether formality of the domain of a non-zero degree map of closed manifolds implies formality of the target. Though there are various situations where this is indeed the case, we show the answer is negative in general, with a counterexample given by a non-zero degree map from a formal manifold to one that carries a non-vanishing quadruple Massey product. This violates a general heuristic that the domain of a non-zero degree map should be more complicated than its target. For the construction of the counterexample we introduce a method to turn a cdga into one that satisfies Poincar\'e duality, which is natural in certain situations.Comment: 15 pages, comments very welcom