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Feb 12, 2018 at 0:53 comment added Michael Freedman This is quite different from the argument I sketch but I like it. Indeed the important detail is giving a finite description of the imbedded 2-spheres building on a finite description of the 1-connected manifold. This is a little tricky, and as far as I see, will still need some work. ( I also do not know how to make the delta-manifold idea precise.) I greatly appreciate the input from Ian, Misha, and Daniele. If the reference I was looking for does not turn up in a couple weeks I will write up something. My present understanding is not succinct enough to just write it out on Mathoverflow.
Feb 10, 2018 at 12:37 history answered Daniele Zuddas CC BY-SA 3.0