Spectral sequences obtained from towers in the infinity category of spectra: décalage, exact couples and Massey products
Summary
There are various ways of constructing spectral sequences from the infinity category of towers of
spectra. Classically there is the approach via exact couples; we will also discuss the décalage functor as
constructed by Hedenlund. We will show that this construction of spectral sequences from towers and
the construction via exact couples give isomorphic spectral sequences. This can be proved by showing
that both methods of can be related to another third construction method by Lurie, using recent work
by Antieau. Furthermore, the décalage construction yields a functor of infinity operads and provides
a way to construct multiplicative spectral sequences. Then we can define Massey products on such
a multiplicative spectral sequence. Lastly, we will discuss a possible relation between these Massey
products and Toda brackets on homotopy groups of spectra, analogous to Moss' theorem for the Adams
spectral sequence.
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