, Volume 245, Issue 1, pp 1-29

Higher homotopy operations

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We provide a general definition of higher homotopy operations, encompassing most known cases, including higher Massey and Whitehead products, and long Toda brackets. These operations are defined in terms of the W-construction of Boardman and Vogt, applied to the appropriate diagram category; we also show how some classical families of polyhedra (including simplices, cubes, associahedra, and permutahedra) arise in this way.

Second author partially supported by grant GA AV ČR 1019203.