5-manifold

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In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.

Non-simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups. Simply connected 5-manifolds were classified by Dennis Barden. Rather surprisingly, this turns out to be easier than the 3- or 4-dimensional case: the 3-dimensional case is the Poincaré conjecture, and the 4-dimensional case is a very hard unsolved problem.

[edit] References

• D. Barden, Simply Connected Five-Manifolds The Annals of Mathematics > 2nd Ser., Vol. 82, No. 3 (Nov., 1965), pp. 365-385