Lie models for the components of sections of a nilpotent fibration

Buijs, Urtzi; Félix, Yves; Murillo, Aniceto

doi:10.1090/S0002-9947-09-04870-3

Lie models for the components of sections of a nilpotent fibration
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by Urtzi Buijs, Yves Félix and Aniceto Murillo PDF

Trans. Amer. Math. Soc. 361 (2009), 5601-5614 Request permission

Abstract:

We give an explicit Lie model for any component of the space of free and pointed sections of a nilpotent fibration, and in particular, of the free and pointed mapping spaces. Among the applications presented, we obtain a Lie model of the exponential law and prove that, in many cases, the rank of the homotopy groups of the mapping space grows at the same rate as the rank of the homotopy groups of the target space.

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