# 3-complexes not embeddable in 3-space

My question is about embeddability of 3-dimensional complexes in R^3. Do we have something like Kuratowski's theorem for complexes in 3-space which specifies a set of minors for non-embeddability?

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Are you asking about 3-dimensional CW complexes? If not, could you let us know what you mean by a "3-dimensional complex". – Ryan Budney Oct 4 '13 at 18:39