# Good Reference for Spanier-Whitehead duality?

Does anyone know of a good book that explains Spanier-Whitehead duality (other than Adams)?

Thanks

Jon

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what do you want to know about it? –  Sean Tilson Oct 22 '11 at 3:11
Well, basically just an introduction to it, which is in Adams I guess (although I feel that it's not as clear as I'd like), but also some explanation of it categorically (i.e. isn't there some notion of it in just a htpy cat. of a model cat or something?) –  Jon Beardsley Oct 24 '11 at 19:57
margolis mentions it in his discussion of the spanier-whitehead category. it seems pretty categorical. –  Sean Tilson Oct 26 '11 at 19:03

Well, one classic source is some exercises in Spanier's book on algebraic topology (alas, I don't have my copy at hand so I can't give a more precise reference, but it is towards the end).

There is also a chapter on it in

MR0273608 (42 #8486) Cohen, Joel M. Stable homotopy. Lecture Notes in Mathematics, Vol. 165 Springer-Verlag, Berlin-New York 1970 v+194 pp.

However, I have to admit that I find Adams's book very clear and beautiful. Is there a reason you don't like it?

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In my edition of Spanier it's Exercise F in chapter 8 on obstruction theory. It is listed in the index. –  t.b. Oct 22 '11 at 9:05
Thanks for this Adam. I haven't spent a great deal of time with Adams' explanation, but I just didn't feel comfortable with it, perhaps I just need to spend some more time with it. Also, I'd like to find it framed in a purely categorical sense, if possible. –  Jon Beardsley Oct 24 '11 at 19:59
Another issue with Adams' definition is that he uses this "join" operation, I believe, is what he means when he writes $S^n\ast S^m$ and I don't really have any intuition about this thing. –  Jon Beardsley Oct 31 '11 at 19:48
The join is something basic and easy, so I would advise you to think about it a bit. It's just a generalization of taking the cone of a space... –  Adam Smith Oct 31 '11 at 20:09
@JBeardz: This is very delayed, but if you are looking for a categorical viewpoint, Spanier-Whitehead duality is a special case of duality in symmetric monoidal categories (though likely you figured this out). –  Akhil Mathew Jan 5 '12 at 18:30

You might find the following interesting: http://www.math.purdue.edu/~gottlieb/Bibliography/53.pdf

even though it is not quite what you asked for.

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+1 for that very nice paper. –  Sigur Aug 15 '14 at 14:52