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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Lie models for the components of sections of a nilpotent fibration

Authors: Urtzi Buijs, Yves Félix and Aniceto Murillo
Journal: Trans. Amer. Math. Soc. 361 (2009), 5601-5614
MSC (2000): Primary 55P62, 54C35
Published electronically: May 29, 2009
MathSciNet review: 2515825
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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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Additional Information

Urtzi Buijs
Affiliation: Departamento de Matemática Aplicada, Campus El Ejido, Universidad de Málaga, 29000 Málaga, Spain

Yves Félix
Affiliation: Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgique

Aniceto Murillo
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080 Málaga, Spain

PII: S 0002-9947(09)04870-3
Keywords: Space of sections, mapping space, Sullivan model, Quillen model, rational homotopy theory
Received by editor(s): February 11, 2008
Published electronically: May 29, 2009
Additional Notes: The first and third authors were partially supported by the Ministerio de Educación y Ciencia grant MTM2007-60016 and by the Junta de Andalucía grant FQM-213
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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