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I am, for whatever reason, interested in learning about the JSJ-decomposition of groups. Having asked around a bit, it was suggested I first learn about what is happening in the manifolds and then read up on the groups stuff. However, I need a reference: I need a book to learn from! Unfortunately, the book which was suggested to me - Hempel's 3-manifolds - is not held by my library, so I was wondering if anyone could perhaps suggest a book which covered the JSJ-decomposition of 3-manifolds (preferably from "the start", as it were), and as an added bonus talks a bit about groups...

(Also, I was contemplating buying Hempel's book, but I am a cheapskate and I've found a version from 1976 which is going cheap. Does anyone know if the book has been updated much since then?)

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First, Hempel's book, though republished by AMS Chelsea, was not updated. In particular, it does not contain anything on the JSJ decomposition! There are two very good sources however on this: Hatcher's (free!) notes on 3-manifolds, available on his website; and Jaco's lecture notes, from the late 1970's. I actually prefer Jaco's notes, because they are so darn intuitive, but they can be hard to find, and it actually does presuppose some stuff from Hempel's book at points. – user641 May 23 '12 at 6:03
I don't think it clicked until now that JSJ decompositions didn't come about until 1977, but Hempel was being published 1976... Anyway, I did somehow find Hatcher's notes, and they seem quite good. For the Jaco notes, are you meaning the book "Lectures on three-manifold topology" (which my library tells me they have!)? – user1729 May 23 '12 at 8:55
Yes, I mean those. He presents in a different style than you might be accustomed to seeing the JSJ decomposition, but all the pieces are there, and IMO is a very nice alternative way to think about it. – user641 May 23 '12 at 18:48
I got the book out today, and it certainly looks interesting. Thanks! – user1729 May 23 '12 at 19:10

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