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Rational homotopy groups and Koszul algebras

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: S. Papadima, A.I. Suciu

Editorial: Comptes Rendus Math'ematique. Acad'emie des Sciences, Paris, 335 (1), p.53-58, 2002.

Rezumat:

Let $X$ and $Y$ be finite-type CW-spaces ($X$ connected, $Y$ simply connected), such that the ring $H^*(Y,QQ)$ is a $k$-rescaling of $H^*(X,QQ)$. If $H^*(X,QQ)$ is a Koszul algebra, then the graded Lie algebra $pi_*(Omega Y)otimes QQ$ is the $k$-rescaling of $gr_*(pi_1 X)otimes QQ$. If $Y$ is a formal space, then the converse holds, and $Y$ is coformal. Furthermore, if $X$ is formal, with Koszul cohomology algebra, there exist filtered group isomorphisms between the Malcev completion of $pi_1 X$, the completion of $[Omega S^{2k+1},Omega Y]$, and the Milnor-Moore group of coalgebra maps from $H_*(Omega S^{2k+1},QQ)$ to $H_*(Omega Y,QQ)$.

Cuvinte cheie: homotopy groups, cohomology ring, lower central series, rescaling, Koszul algebras

URL: http://dx.doi.org/10.1016/S1631-073X(02)02420-2