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In the late 1970's and in the 1980's, Michael Freedman showed a relationship between the topological surgery problem in 4-dimensions, the slice problem for links, and the classification of non-simply-connected 4-manifolds. He also showed the failure of 4-dimensional homology surgery and the homology splitting theorem via a construction I don't really follow (because I haven't read and don't know the original reference, for one thing). I know of these results vaguely but do not understand them (certainly not the proofs). In particular, I don't know the "canonical" references, and MathSciNet doesn't seem to be helping me. They look like basic results in 4-manifold topology, which should surely be standard. Is there a survey paper on this stuff, or is it in some book? What is the best reference?
I should know this (or look it up myself), but perhaps it is more useful to post it here, because perhaps I am not alone in my confusion.

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I would recommend you to look at the reference Freedman-Quinn book Topology of 4-manifolds , it might be helpful.

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  • $\begingroup$ Also, if you're looking for original references, do a MathSciNet search Author="Freedman, Michael H" in the date range 1982-1986. Here is a link to my search: ams.org/mathscinet/search/… $\endgroup$
    – Ryan Budney
    Commented Feb 8, 2010 at 15:36

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