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Formality of function spaces  Micheline ViguéPoirrier
;  Date: 
1 May 2007  Subject:  Algebraic Topology (math.AT)  Abstract:  Let $X$ be a nilpotent space such that there exists $pgeq 1$ with
$H^p(X,mathbb Q)
e 0$ and $H^n(X,mathbb Q)=0$ if $n>p$. Let $Y$ be a
mconnected space with $mgeq p+1$ and $H^*(Y,mathbb Q)$ is finitely generated
as algebra. We assume that $X$ is formal and there exists $p$ odd such that
$H^p(X,mathbb Q)
e 0$. 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 $mathcal F(S^2,Y)$ where $Y$ is not rationally
equivalent to a product of Eilenberg Mac Lane spaces.  Source:  arXiv, arxiv.0705.0144  Services:  Forum  Review  PDF  Favorites 


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