, Volume 26, Issue 2, pp 573-588
Date: 28 Sep 2012

\(L_{\infty }\) rational homotopy of mapping spaces

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.