Sur l'homotopie rationnelle des espaces fonctionnels |
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Authors: | Micheline Vigué-Poirrier |
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Institution: | (1) 37, Parc d'Ardenay, 91120 Palaiseau, France |
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Abstract: | Let X be a nilpotent space such that it exists k 1 with Hp (X, ) = 0 p > k and Hk (X, ) 0, let Y be a (m–1)-connected space with m k+2, then the rational homotopy Lie algebra of YX (resp.
is isomorphic as Lie algebra, to H* (X, ) ( * ( Y) ) (resp.+ (X, ) ( * ( Y) )). If X is formal and Y -formal, then the spaces YX and
are -formal. Furthermore, if dim * ( Y) is infinite and dim H* (Y,Q) is finite, then the sequence of Betti numbers of
grows exponentially. |
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Keywords: | |
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