A model for the Whitehead product in rational mapping spaces

TL;DR

This paper models the Whitehead product in rational mapping spaces using André-Quillen cohomology, providing a new algebraic framework and an upper bound for the Whitehead length of these spaces.

Contribution

It introduces a novel algebraic description of Whitehead products in rational mapping spaces via André-Quillen cohomology, linking homotopy and cohomology theories.

Findings

Whitehead products characterized in terms of André-Quillen cohomology

Upper bound established for Whitehead length of mapping spaces

Provides algebraic tools for analyzing rational homotopy groups

Abstract

We describe the Whitehead products in the rational homotopy group of a connected component of a mapping space in terms of the Andr\'{e}-Quillen cohomology. As a consequence, an upper bound for the Whitehead length of a mapping space is given.