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I am working on a subject of geometric group theory closely related to 3-manifolds, and in order to understand these links, I am seeking a good reference about 3-manifolds, as self-contained as possible, and in particular dealing with: loop and sphere theorems, Heegaard diagrams, Haken manifolds.

I browsed Hempel's book, 3-manifolds, but a lot of PL topology seems to be assumed. As pointed out when I asked the same question on math.stackexchange, it is probably the case for any book on 3-manifods, so a good reference on PL topology as complement would be welcome.

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    $\begingroup$ Rolfsen's "Knots and Links" is a classic, with lots of nice pictures and geometric intuition. It covers all the topics you mention, other than Haken manifolds. $\endgroup$
    – Mark Grant
    Commented Mar 14, 2014 at 10:34
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    $\begingroup$ Hatcher's 3-manifolds notes would also be good, although they assume you're fairly well grounded in basic manifold theory, in either the smooth or PL categories. There's also Jaco's CBMS "Lectures on 3-manifold topology". $\endgroup$
    – Ryan Budney
    Commented Mar 14, 2014 at 16:40
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    $\begingroup$ A lesser known source is Fomenko-Matveev's book "Algorithmic and computer methods for three-manifolds". Despite its title, it has nothing to do with computers, but instead is a very nice basic course on 3-manifold topology. The pictures in it are really wonderful. $\endgroup$
    – Andy Putman
    Commented Mar 14, 2014 at 18:27

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For the sake having an official answer, as opposed to a comment-as-answer, I'll second Mark Grant's suggestion of Rolfsen's "Knots and Links". It was the first book I read on 3-manifold topology, and I enjoyed it very much.

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Jennifer Schultens has written a notes on 3-manifolds, see https://www.math.ucdavis.edu/~jcs/pubs/notes.pdf.

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  • $\begingroup$ Her book will be soon available amazon.com/… $\endgroup$
    – Seirios
    Commented May 9, 2014 at 9:40
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Why nobody mentions Thurston's book "Three-Dimensional Geometry and Topology"?

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    $\begingroup$ It is a wonderful and inspirational book, but it does not cover the topics listed in the post. $\endgroup$
    – Andy Putman
    Commented Jan 20, 2018 at 3:32
  • $\begingroup$ Oops. Sorry. The book written by Cheeger and Erin "Comparison Theorems in Riemannian Geometry" has two chapters on Sphere theorem. Recently, "Ricci Flow and sphere theorem" written by Brendle. $\endgroup$
    – user106560
    Commented Jan 20, 2018 at 3:57
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    $\begingroup$ The sphere theorem in the two books you discuss is en.wikipedia.org/wiki/Sphere_theorem, while the sphere theorem discussed in the question is en.wikipedia.org/wiki/Sphere_theorem_(3-manifolds). Though they are known by the same name, they are completely unrelated. $\endgroup$
    – Andy Putman
    Commented Jan 20, 2018 at 4:02
  • $\begingroup$ I heard that John H. Hubbard is working on a book on Haken manifolds, Volume 4 of a series of 4 volumes. I read some chapters of Volume 1 of "Teichmuller theory" written by him. It is a very good book. I hope Hubbard will release Volume 3 and 4 soon. $\endgroup$
    – user106560
    Commented Jan 20, 2018 at 4:02
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    $\begingroup$ I agree that Hubbard's first book is really wonderful (I own the second, but have not read much of it). The stuff about Haken manifolds will be in the fourth, but my impression is that this will not be complete any time soon. $\endgroup$
    – Andy Putman
    Commented Jan 20, 2018 at 4:04

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