Higher order Toda brackets

Aziz Kharoof

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arXiv · 2010.15961

Higher order Toda brackets

Aziz Kharoof

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Abstract

We describe two ways to define higher order Toda brackets in a pointed simplicial model category $\mathcal{D}$: one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment. We show that these two definitions agree, by providing a third, diagrammatic, description of the Toda bracket, and explain how it serves as the obstruction to rectifying a certain homotopy-commutative diagram in $\mathcal{D}$.

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Aziz Kharoof. 2020-10-29. Higher order Toda brackets. https://arxiv.org/abs/2010.15961

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