Moise's theorem

Short description: Any topological 3-manifold has unique PL and smooth structures

In geometric topology, a branch of mathematics, Moise's theorem, proved by Edwin E. Moise in (Moise 1952), states that any topological 3-manifold has an essentially unique piecewise-linear structure and smooth structure.

The analogue of Moise's theorem in dimension 4 (and above) is false: there are topological 4-manifolds with no piecewise linear structures, and others with an infinite number of inequivalent ones.

See also

• Exotic sphere

References

• Moise, Edwin E. (1952), "Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung", Annals of Mathematics, Second Series 56: 96–114, doi:10.2307/1969769, ISSN 0003-486X 
• Moise, Edwin E. (1977), Geometric topology in dimensions 2 and 3, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90220-3