2007/05/01 by Micheline Vigué-Poirrier, Vigué-Poirrier, Micheline
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.0705.0144
Let X be a nilpotent space such that there exists p≥ 1 with Hp(X,\mathbb Q) ≠ 0 and Hn(X,\mathbb Q)=0 if n>p. Let Y be a m-connected space with m≥ p+1 and H^*(Y,\mathbb Q) is finitely generated as algebra. We assume that X is formal and there exists p odd such that Hp(X,\mathbb Q) ≠ 0. We prove that if the space \mathcal F(X,Y) of continuous maps from X to Y is formal, then Y has the rational homotopy type of a product of Eilenberg Mac Lane spaces. At the opposite, we exhibit an example of a formal space \mathcal F(S2,Y) where Y is not rationally equivalent to a product of Eilenberg Mac Lane spaces.