L_infty rational homotopy of mapping spaces

2012/09/21 by Buijs, Urtzi, Félix, Yves, Murillo, Aniceto
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1209.4756

Abstract

In this paper we describe explicit L_∞ algebras modeling the rational homotopy type of any component of the spaces \map(X,Y) and \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_∞ algebras model the universal covers of the corresponding mapping spaces.

Related

• Algebraic Hopf invariants and rational models for mapping spaces
• Rational formality of mapping spaces
• Rational homotopy type of mapping spaces via cohomology algebras
• Algebraic models of non-connected spaces and homotopy theory of\n L_\∞ algebras
• Cohomology C_∞-algebra and Rational Homotopy Type