Classification of Compact Two-Manifolds/Lemma


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Lemma for Classification of Compact Two-Manifolds

A compact, boundaryless $2$-manifold $S$ is diffeomorphic to a polyhedral disk $P$ with edges identified pairwise.

That is, for any closed, connected $2$-manifold, there exists a polyhedral disk $P$ and an equivalence relation $\sim$ such that:

$S \cong P \setminus \sim$


Proof


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