Is there a rigorous proof of the classification theorem for compact (connected) two-manifolds that describe all of them up to a homeomorphism? I have seen many books and all of them use way too much hand waving. All the current proofs that I seen rely way too much on drawing pictures. Is there an actual rigorous proof which cleanly defines all the concepts and establishes the classification theorem without any hand-waving nor appealing to pictures?
2026-04-09 00:22:37.1775694157
Classification of Compact Surfaces
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Sure. Take a look at André Gramain's Topology of Surfaces. I will find here a list of textbooks which contain a proof of the classification.