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Formality criteria in terms of higher Whitehead brackets

MPG-Autoren
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Moreno-Fernández,  José M.
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1902.03034.pdf
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Zitation

Buijs, U., & Moreno-Fernández, J. M. (2019). Formality criteria in terms of higher Whitehead brackets. Topology and its Applications, 267: 106901. doi:10.1016/j.topol.2019.106901.


Zitierlink: https://hdl.handle.net/21.11116/0000-0005-0B30-9
Zusammenfassung
We provide two criteria for establishing the non-formality of a differential graded Lie algebra in terms of higher Whitehead brackets, which are the Lie analogues 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.