MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.