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The classification of real projective structures on compact surfaces
Real projective structures ($\mathbb {RP}$-structures) on compact surfaces are classified. The space of projective equivalence classes of real projective structures on a closed orientable surface of genus $g>1$ is a countable disjoint union of open cells of dimension $16g-16$. A key idea is Choi's admissible decomposition of a real projective …