The classification of real projective structures on compact surfaces

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Real projective structures (RP2-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 structure into convex subsurfaces along closed geodesics. The deformation space of convex structures forms a connected component in the moduli space of representations of the fundamental group in PGL(3, R), establishing a conjecture of Hitchin.
Publisher
AMER MATHEMATICAL SOC
Issue Date
1997-04
Language
English
Article Type
Article
Citation

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, v.34, no.2, pp.161 - 171

ISSN
0273-0979
DOI
10.1090/S0273-0979-97-00711-8
URI
http://hdl.handle.net/10203/75263
Appears in Collection
MA-Journal Papers(저널논문)
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