Algebraic and Geometric Topology 5 (2005), paper no. 29, pages 713-724.

H-space structure on pointed mapping spaces

Yves Felix and Daniel Tanre

Abstract. We investigate the existence of an H-space structure on the function space, F_*(X,Y,*), of based maps in the component of the trivial map between two pointed connected CW-complexes X and Y. For that, we introduce the notion of H(n)-space and prove that we have an H-space structure on F_*(X,Y,*) if Y is an H(n)-space and X is of Lusternik-Schnirelmann category less than or equal to n. When we consider the rational homotopy type of nilpotent finite type CW-complexes, the existence of an H(n)-space structure can be easily detected on the minimal model and coincides with the differential length considered by Y. Kotani. When X is finite, using the Haefliger model for function spaces, we can prove that the rational cohomology of F_*(X,Y,*) is free commutative if the rational cup length of X is strictly less than the differential length of Y, generalizing a recent result of Y. Kotani.

Keywords. Mapping spaces, Haefliger model, Lusternik-Schnirelmann category

AMS subject classification. Primary: 55R80, 55P62, 55T99.

E-print: arXiv:math.AT/0507147

DOI: 10.2140/agt.2005.5.713

Submitted: 13 February 2005. Accepted: 30 June 2005. Published: 5 July 2005.

Notes on file formats

Yves Felix Daniel Tanre
Departement de Mathematiques, Universite Catholique de Louvain
2, Chemin du Cyclotron, 1348 Louvain-La-Neuve, Belgium
Departement de Mathematiques, UMR 8524, Universite de Lille 1
59655 Villeneuve d'Ascq Cedex, France


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