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.
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 0048805
moise, theorem, geometric, topology, branch, mathematics, proved, edwin, moise, moise, 1952, states, that, topological, manifold, essentially, unique, piecewise, linear, structure, smooth, structure, analogue, dimension, above, false, there, topological, manif. 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 EditExotic sphereReferences EditMoise 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 0048805 Moise Edwin E 1977 Geometric topology in dimensions 2 and 3 Berlin New York Springer Verlag ISBN 978 0 387 90220 3 MR 0488059 This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Moise 27s theorem amp oldid 1016301168, wikipedia, wiki, book, books, library,
