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 {{harvtxt|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== *{{Citation | last1=Moise | first1=Edwin E. | title=Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung | jstor=1969769 | mr=0048805 | year=1952 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=56 | pages=96–114 | doi=10.2307/1969769}} *{{Citation | last1=Moise | first1=Edwin E. | title=Geometric topology in dimensions 2 and 3 | publisher=Springer-Verlag | location=Berlin, New York | isbn=978-0-387-90220-3 | mr=0488059 | year=1977}}

Category:Geometric topology

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