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January, 2010 Whitehead products in function spaces: Quillen model formulae
Gregory LUPTON, Samuel Bruce SMITH
J. Math. Soc. Japan 62(1): 49-81 (January, 2010). DOI: 10.2969/jmsj/06210049


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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Gregory LUPTON. Samuel Bruce SMITH. "Whitehead products in function spaces: Quillen model formulae." J. Math. Soc. Japan 62 (1) 49 - 81, January, 2010.


Published: January, 2010
First available in Project Euclid: 5 February 2010

zbMATH: 1193.55005
MathSciNet: MR2648216
Digital Object Identifier: 10.2969/jmsj/06210049

Primary: 55P62 , 55Q15

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

Rights: Copyright © 2010 Mathematical Society of Japan


Vol.62 • No. 1 • January, 2010
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