The classification of surfaces via normal curves
arXiv:2208.00999 · doi:10.1365/s13291-022-00265-5
Abstract
We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser's and Milnor's proof of the existence and uniqueness of the prime decomposition of 3-manifolds. In particular, we do not need any invariants from algebraic topology to distinguish surfaces.
12 pages, 7 figures; V2: Corrected an error in Section 5 and added discussion about nonorientable surfaces