Journal of the Mathematical Society of Japan

Whitehead products in function spaces: Quillen model formulae

Gregory LUPTON and Samuel Bruce SMITH

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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.

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 1 (2010), 49-81.

Dates
First available in Project Euclid: 5 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1265380424

Digital Object Identifier
doi:10.2969/jmsj/06210049

Mathematical Reviews number (MathSciNet)
MR2648216

Zentralblatt MATH identifier
1193.55005

Subjects
Primary: 55P62: Rational homotopy theory 55Q15: Whitehead products and generalizations

Keywords
Whitehead product function space Quillen minimal model derivation coformal space Whitehead length

Citation

LUPTON, Gregory; SMITH, Samuel Bruce. Whitehead products in function spaces: Quillen model formulae. J. Math. Soc. Japan 62 (2010), no. 1, 49--81. doi:10.2969/jmsj/06210049. https://projecteuclid.org/euclid.jmsj/1265380424


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