Moise's theorem

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, JSTOR 1969769, MR 004880596-114&rft.date=1952&rft.issn=0003-486X&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=0048805#id-name=MR&rft_id=https://www.jstor.org/stable/1969769#id-name=JSTOR&rft_id=info:doi/10.2307/1969769&rft.aulast=Moise&rft.aufirst=Edwin E.&rfr_id=info:sid/en.wikipedia.org:Moise's theorem" class="Z3988">
• Moise, Edwin E. (1977), Geometric topology in dimensions 2 and 3, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90220-3, MR 0488059