<i>L</i><sub>∞</sub> models of based mapping spaces

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  • Buijs Urtzi
    Universidad de Málaga, Departamento de Matemática Aplicada
  • Félix Yves
    Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée
  • Murillo Aniceto
    Universidad de Málaga, Departamento de Álgebra, Geometría y Topología

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  • L∞ models of based mapping spaces
  • Linfinity models of based mapping spaces

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Abstract

In this paper, for any pointed map f : X → Y between finite type nilpotent CW-complexes, we obtain L∞ and Lie models of mapf*(X,Y), the pointed space of based maps homotopic to f, in terms of Lie algebras constructed from the Quillen models of X and Y. The main advantage of our approach is to allow X to be an infinite dimensional CW-complex, in which case mapf*(X,Y) has no longer the homotopy type of a finite type CW-complex.

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