Suppose that $M$ closed orientable 2-manifold and $\chi (M) = 2$. Why is $M$ a sphere?
I want a prove with triangulation.
2026-03-29 14:28:09.1774794489
Closed orientable 2-manifold
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By classification of surfaces, two closed orientable surfaces are homeomorphic if and only if their Euler characteristics agree. To show that $\chi(S^2) = 2$, consider a vertex with a loop to itself (1 edge), then glue two discs (2 faces) with disjoint interiors along the loop.