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In an old answer to an old question of mine, Peter Teichner commented that it is an open problem to determine which homotopy 2-types arise from 4-manifolds. In some instances we know that a 4-manifold is a 2-type with one extra piece of data (the intersection form), so it's a very interesting question as to when we can go the other way.

I'd like to know what is the latest on this problem, in the form of references or results.

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When you say "in some instances", do you mean "in the simply connected case"? –  S. Carnahan Feb 1 '13 at 14:00
No. There are nontrivial cases known for $\pi_1\not=0$. –  David Roberts Feb 2 '13 at 11:06

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