, Volume 26, Issue 2, pp 573-588

$L_{\infty }$ rational homotopy of mapping spaces

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

In this paper we describe explicit $L_\infty $ algebras modeling the rational homotopy type of any component of the spaces $\text{ map}(X,Y)$ and $\text{ map}^*(X,Y)$ of free and pointed maps between the finite nilpotent CW-complex $X$ and the finite type nilpotent CW-complex $Y.$ When $X$ is of finite type, non necessarily finite, we also show that the algebraic covers of these $L_\infty $ algebras model the universal covers of the corresponding mapping spaces.

U. Buijs was partially supported by the MICIN grant MTM2010-15831 and by the Junta de Andalucía grant FQM-213, Y. Félix was partially supported by the MICIN grant MTM2010-18089 and A. Murillo was partially supported by the MICIN grant MTM2010-18089 and by the Junta de Andalucía grants FQM-213 and P07-FQM-2863.