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I want to study P & J homomorphisms and Hopf invariant in Homotopy theory.

I have some paper, but I don't know what is first and what is nice.

Please recommend to me.

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  • $\begingroup$ George Whitehead's book on homotopy theory, perhapes. $\endgroup$
    – Fernando Muro
    Commented Sep 21, 2011 at 11:29
  • $\begingroup$ Is P the one in EHP? $\endgroup$
    – Sean Tilson
    Commented Sep 22, 2011 at 2:34
  • $\begingroup$ Tilson/ Yes. P is the Whitehead product homomorphism. $\endgroup$
    – Jino
    Commented Sep 22, 2011 at 5:58

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Doug Ravenel's "Complex Cobordism and the Stable Homotopy Groups of Spheres" does a nice job with the J-homomorphism and the Hopf Invariant, as well as a whole lot more. I don't recall if he talks about the P-homomorphism. This book is colloquially called the Green Book, but the second edition is actually red.

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  • $\begingroup$ Thank you. I'll study the Green book. How many knowledge needed to read this book? $\endgroup$
    – Jino
    Commented Sep 22, 2011 at 6:00
  • $\begingroup$ Makes you wonder about publishing houses... $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Sep 22, 2011 at 6:38
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    $\begingroup$ I finally found my copy of Ravenel. He does cover the EHP spectral sequence, so he discusses the P-homomorphism. I'd say this book requires quite a bit of mathematical maturity to read. The book that best prepared me was by Mosher and Tangora. Even if you don't read that one, you should probably learn about spectral sequences somewhere else first before tackling Ravenel. The ideal way to read Ravenel is with a pencil in hand filling in the spectral sequence diagrams he scatters throughout. $\endgroup$
    – David White
    Commented Sep 22, 2011 at 13:18
  • $\begingroup$ I know this answer is old, but I wanted to point out that the book is available online $\endgroup$
    – Denis Nardin
    Commented Jan 17, 2017 at 19:55
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The lecture I gave in Bonn in 2008 http://www.maths.ed.ac.uk/~aar/slides/bonn3.pdf is an introduction to the Hopf invariant and its applications.

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I recommend a lecture note by Fred Cohen for the EHP sequence, although it doesn't explain the J homomorphism.

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