I am loking for a reference to the following fact
The fundamental group of a non-closed surface is free.
2026-03-29 03:18:59.1774754339
Reference request: fundamental groups
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Take a look at this question on MathOverflow. It's about the noncompact case, but that suffices for your question because any non-closed surface is homotopy equivalent to its interior, which is a noncompact surface.