$L_{i}nfty$ 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 $\map(X,Y)$ 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 $L_{\infty }$ algebras model the universal covers of the corresponding mapping spaces.

arXiv comment19 pages

References in corpus (2)

• Deformation quantization of Poisson manifolds, I
• Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras

Cited by in corpus (1)

• T-duality in rational homotopy theory via $L_{\infty }$-algebras