Evaluation maps in rational homotopy

Félix, Yves;Lupton, Gregory
(2007) Topology — Vol. 46, n° 5, p. 493-506 (2007)

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Authors
  • Félix, YvesUCLouvain
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  • Lupton, Gregory
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Abstract
In the rational category of nilpotent complexes, let E be an H-space acting on a space X. With mild hypotheses we show that the action on the base point w: E -> X factors through a map Gamma(E): S-E -> X, where S-E is a finite product of odd-dimensional spheres and FE is a homotopy monomorphism. Among others, the following consequences are obtained: pi(*)(w) # 0 if and only if w is essential and H-*(w) not equal 0 if and only if X satisfies a strong splitting condition. (C) 2007 Elsevier Ltd. All rights reserved.
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Félix, Y., & Lupton, G. (2007). Evaluation maps in rational homotopy. Topology, 46(5), 493-506. https://doi.org/10.1016/j.top.2007.03.005 (Original work published 2007)