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A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.

4 votes

Surjections from genus $n$ surface group to free group of rank $n$

I think this result can be found in ``Heegard splittings and splitting homomorphisms",by W.Jaco, Trans. Amer. Math. Soc. 144 (1969),365--379.
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