Smooth structures on closed $3$-manifolds are unique up to diffeomorphism?

Hi!

I'm using the theorem stated in the question, but so far, I haven't found a source that does explicitely state and prove it or at least give a proper citation. It must be me though, since the theorem seems rather well-established.

So far, I have found dmoskovich's blog and a few papers by googling that are using the theorem as well.

Any pointers to a source that explicitely states and proves the above theorem are appreciated. I need the citation for my thesis, so I don't think I'm allowed to take any hints on how to actually prove the theorem :)

Thanks!

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1 Answer

This is Moise's Theorem. See the Wikipedia page, where you will find the following references to the literature:

Moise, Edwin E. (1952), "Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung", Annals of Mathematics. Second Series 56: 96–114, ISSN 0003-486X, JSTOR 1969769, MR0048805

Moise, Edwin E. (1977), Geometric topology in dimensions 2 and 3, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90220-3, MR0488059

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