Open Access
November 2008 An estimate in Gottlieb ranks of fibration
Toshihiro Yamaguchi
Bull. Belg. Math. Soc. Simon Stevin 15(4): 663-675 (November 2008). DOI: 10.36045/bbms/1225893946


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.


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Toshihiro Yamaguchi. "An estimate in Gottlieb ranks of fibration." Bull. Belg. Math. Soc. Simon Stevin 15 (4) 663 - 675, November 2008.


Published: November 2008
First available in Project Euclid: 5 November 2008

zbMATH: 1211.55009
MathSciNet: MR2475490
Digital Object Identifier: 10.36045/bbms/1225893946

Primary: 55P62 , 55Q70 , 55R05

Keywords: Gottlieb homology group , Gottlieb sequence of fibration , Gottlieb type , rational Gottlieb group , Sullivan minimal model

Rights: Copyright © 2008 The Belgian Mathematical Society

Vol.15 • No. 4 • November 2008
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