Formality criteria in terms of higher Whitehead brackets

Urtzi Buijs; José M. Moreno-Fernández

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arXiv · 1902.03034

Formality criteria in terms of higher Whitehead brackets

Urtzi Buijs·José M. Moreno-Fernández

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Abstract

We provide two criteria for discarding the formality of a differential graded Lie algebra in terms of higher Whitehead brackets, which are the Lie analogue of the Massey products of a differential graded associative algebra. We also show that formality of a differential graded Lie algebra is not equivalent to the collapse of the Quillen spectral sequence. Finally, we use $L_\infty$ algebras and Quillen's formulation of rational homotopy theory to recover and improve a classical theorem for detecting higher Whitehead products in Sullivan minimal models and give some applications.

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Urtzi Buijs, José M. Moreno-Fernández. 2019-02-08. Formality criteria in terms of higher Whitehead brackets. https://arxiv.org/abs/1902.03034

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