Toda brackets are a type of higher homotopy operation. Like Massey
products, they are not always defined, and their value is
indeterminate. Nevertheless, they play an important role in algebraic
topology and related fields:
Toda originally constructed them as a tool for computing homotopy groups
of spheres. Adams later showed that
they can be used to calculate differentials in spectral sequences.
After reviewing the construction and properties of the classical Toda
bracket, we shall describe a higher order version
the construction will be explained using simple examples for chain
complexes.
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