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Higher homotopy operations. (English) Zbl 1038.55011

The authors define higher order homotopy operations as the obstruction to making a homotopy-commutative diagram of spaces strictly commutative. This obstruction is defined in terms of the \(W\)-construction of Boardmam-Vogt. In so doing they present a uniform treatment of the main known examples. Giving an explicit dictionary for translating between the cohomology obstructions provided by Dwyer, Kan and Smith and the description provided here in terms of higher operations would be an interesting question.

MSC:

55S35 Obstruction theory in algebraic topology
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