naa a22 4500 510760813 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s13163-012-0105-z doi (NATIONALLICENCE)springer-10.1007/s13163-012-0105-z $$L_{\infty }$$ rational homotopy of mapping spaces [Elektronische Daten] [Urtzi Buijs, Yves Félix, Aniceto Murillo] 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. Universidad Complutense de Madrid, 2012 Mapping space nationallicence Rational homotopy theory nationallicence $$L_\infty $$ algebra nationallicence $$L_\infty $$ model of a space nationallicence Buijs Urtzi Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Louvain, Belgium aut Félix Yves Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Louvain, Belgium aut Murillo Aniceto Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080, Málaga, Spain aut Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 573-588 1139-1138 26:2<573 2013 26 13163 https://doi.org/10.1007/s13163-012-0105-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-012-0105-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buijs Urtzi Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Louvain, Belgium aut NATIONALLICENCE 700 1- Félix Yves Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Louvain, Belgium aut NATIONALLICENCE 700 1- Murillo Aniceto Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080, Málaga, Spain aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 573-588 1139-1138 26:2<573 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer