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Lie models for the components of sections of a nilpotent fibration
Author(s):
Urtzi
Buijs;
Yves
Félix;
Aniceto
Murillo
Journal:
Trans. Amer. Math. Soc.
361
(2009),
5601-5614.
MSC (2000):
Primary 55P62, 54C35
Posted:
May 29, 2009
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Additional information
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
Email:
urtzi@agt.cie.uma.es
Yves
Félix
Affiliation:
Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, Universit{é Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgique
Email:
felix@math.ucl.ac.be
Aniceto
Murillo
Affiliation:
Departamento de Álgebra, Geometr{\'i}a y Topología, Universidad de Málaga, Ap. 59, 29080 Málaga, Spain
Email:
aniceto@agt.cie.uma.es
DOI:
10.1090/S0002-9947-09-04870-3
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
Posted:
May 29, 2009
Additional Notes:
The first and third authors were partially supported by the {\em Ministerio de Educación y Ciencia} grant MTM2007-60016 and by the Junta de Andalucía grant FQM-213
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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