Whitehead products in function spaces: Quillen model formulae

2008/12/10 by Gregory Lupton, Lupton, Gregory, Samuel Bruce Smith +1
Mathematics · #55P62 #55Q15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0812.1829

openalex publication_date 2008/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Whitehead products in the rational homotopy groups of a general component of a function space. For the component of any based map f: X → Y, in either the based or free function space, our main results express the Whitehead product directly in terms of the Quillen minimal model of f. These results follow from a purely algebraic development in the setting of chain complexes of derivations of differential graded Lie algebras, which is of interest in its own right. We apply the results to study the Whitehead length of function space components.

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