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2005 $H$–space structure on pointed mapping spaces
Yves Félix, Daniel Tanre
Algebr. Geom. Topol. 5(2): 713-724 (2005). DOI: 10.2140/agt.2005.5.713

Abstract

We investigate the existence of an H–space structure on the function space, (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 (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 (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.

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Yves Félix. Daniel Tanre. "$H$–space structure on pointed mapping spaces." Algebr. Geom. Topol. 5 (2) 713 - 724, 2005. https://doi.org/10.2140/agt.2005.5.713

Information

Received: 13 February 2005; Revised: 18 April 2006; Accepted: 30 June 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1082.55006
MathSciNet: MR2153111
Digital Object Identifier: 10.2140/agt.2005.5.713

Subjects:
Primary: 55P62, 55R80, 55T99

Rights: Copyright © 2005 Mathematical Sciences Publishers

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