An estimate in Gottlieb ranks of fibration
Yamaguchi, Toshihiro
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 663-675 / Harvested from Project Euclid
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As an application of the Gottlieb sequence of fibration, we give an upper bound of the rank of Gottlieb group $G(E) =\oplus_{i>0}G_i(E)$ of the total space $E$ of a fibration $\xi :X\to E\to B$ and define the {\it Gottlieb type $(a,b,c;s,t,u)$}, which describes a rational homotopical condition of fibration with $\rank G(E)=s+t+u$. We also note various examples showing the different situations that can occur. Finally we comment about an interaction with a Halperin's conjecture on fibration.
Publié le : 2008-05-15
Classification:  rational Gottlieb group,  Gottlieb sequence of fibration,  Gottlieb homology group,  Gottlieb type,  Sullivan minimal model,  55P62,  55R05,  55Q70 
@article{1225893946,
     author = {Yamaguchi, Toshihiro},
     title = {An estimate in Gottlieb ranks of fibration},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 663-675},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1225893946}
}

Yamaguchi, Toshihiro. An estimate in Gottlieb ranks of fibration. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  663-675. http://gdmltest.u-ga.fr/item/1225893946/