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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.

edited Sep 21 2011 at 13:55

David White
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asked Sep 21 2011 at 9:34

Jino
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George Whitehead's book on homotopy theory, perhapes. – Fernando Muro Sep 21 2011 at 11:29

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I retagged. Also, this should be community wiki – David White Sep 21 2011 at 13:56

Is P the one in EHP? – Sean Tilson Sep 22 2011 at 2:34

Thanks Muro. i'll study Whitehead's book. – Jino Sep 22 2011 at 5:50

Tilson/ Yes. P is the Whitehead product homomorphism. – Jino Sep 22 2011 at 5:58

David White · Answer 1 · 2011-09-21 13:55:36Z UTC

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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.

answered Sep 21 2011 at 13:55

David White
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Thank you. I'll study the Green book. How many knowledge needed to read this book? – Jino Sep 22 2011 at 6:00

Makes you wonder about publishing houses... – Mariano Suárez-Alvarez Sep 22 2011 at 6:38

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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. – David White Sep 22 2011 at 13:18

Andrew Ranicki · Answer 2 · 2011-09-22 05:59:55Z UTC

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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.

answered Sep 22 2011 at 5:59

Andrew Ranicki
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Dai Tamaki · Answer 3 · 2011-09-27 05:54:50Z UTC

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

answered Sep 27 2011 at 5:54

Dai Tamaki
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What is the best paper or book studying the P homomorphism, J homomorphism and Hopf invariant in Homotopy theory?

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