In
geometric topology
In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another.
History
Geometric topology as an area distinct from algebraic topo ...
, a branch of mathematics, Moise's theorem, proved by
Edwin E. Moise in , states that any topological
3-manifold
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (geometry), plane (a tangent ...
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
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Geometric topology
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