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I have added some bare minimum content to EHP spectral sequence.
Please forgive my ignorance. What’s the map $P$?
Todd, it’s just the homotopy fiber of the map $E$, 2-locally. James’ result is the construcion of the map $H$ and the proof that $E$, in turn, is the homotopy fiber of $H$, 2-locally. Hence you may think of $P$ as being the connecting homomorphism induced by the James fibration.
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