Rational formality of function spaces
| dc.creator | Vigue-Poirrier, Micheline | |
| dc.date | 2007-06-20 | |
| dc.date.accessioned | 2026-07-07T08:11:20Z | |
| dc.date.available | 2026-07-07T08:11:20Z | |
| dc.description | Let $X$ be a nilpotent space such that there exists $N\geq 1$ with $H^N(X,\mathbb Q) \ne 0$ and $H^n(X,\mathbb Q)=0$ if $n>N$. Let $Y$ be a m-connected space with $m\geq N+1$ and $H^*(Y,\mathbb Q)$ is finitely generated as algebra. We assume that the odd part of the rational Hurewicz homomorphism: $π_{odd}(X)\otimes \mathbb Q\to H_{odd}(X,\mathbb Q)$ 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 $\mathcal F(S^2,Y)$ where $Y$ is not rationally equivalent to a product of Eilenberg Mac Lane spaces. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0706.2977 | |
| dc.identifier | http://arxiv.org/abs/0706.2977 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132090 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P62;55P35 | |
| dc.title | Rational formality of function spaces | |
| dc.type | text |