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Nov 17, 2012 at 0:31 comment added Peter May I sympathize with "there is sooo muuuch literature''. The people who do the most calculational of calculational work really do use Massey products and Toda brackets (I have one student working that way right now). Look at papers of Mahowald and collaborators to see more such things in action, for example papers on the Kervaire invariant one problem in dimensions 30 and 62 (but they may be hard reading).
Nov 16, 2012 at 21:41 comment added Joseph Victor Thank you for the response. I apologize because I am a still learning the literature and am probably missing some important point. In H_\infty ring spectra and applications, Bruner does not seem to use Massey Products at all, unless it is in some subtle way I cannot pick up on. He writes down a lot of Massey products, even citing a theorem about their interactions with Steenrod Squares, but does not seem to actually use them for computations. The same holds for Milgram's big paper on the topic, and this is what confuses me.
Nov 16, 2012 at 21:35 vote accept Joseph Victor
Nov 16, 2012 at 17:54 history answered Peter May CC BY-SA 3.0