2007/06/20 by Micheline Vigué-Poirrier, Micheline Vigue-Poirrier, Vigue-Poirrier, Micheline
Mathematics · #55P35 #55P62 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P35 #msc:55P62
paper · pdf · doi:10.48550/arxiv.0706.2977
10 pages
arxiv created 2007/06/20 · openalex publication_date 2007/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a nilpotent space such that there exists N≥ 1 with HN(X,\mathbb Q) ≠ 0 and Hn(X,\mathbb Q)=0 if n>N. Let Y be a m-connected space with m≥ N+1 and H^*(Y,\mathbb Q) is finitely generated as algebra. We assume that the odd part of the rational Hurewicz homomorphism: πodd(X)⊗ \mathbb Q→ Hodd(X,\mathbb Q) is non-zero. We prove that if the space \mathcal F(X,Y) of continuous maps from X to Y is rationally formal, then Y has the rational homotopy type of a finite product of Eilenberg Mac Lane spaces. At the opposite, we exhibit an example of a rationally formal space \mathcal F(S2,Y) where Y is not rationally equivalent to a product of Eilenberg Mac Lane spaces.