Bulletin of the American Mathematical Society

Author(s): Suhyoung Choi; William M. Goldman
Journal: Bull. Amer. Math. Soc. 34 (1997), 161-171.
MSC (1991): Primary 57M05, 53A20
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Abstract: Real projective structures ( ${\Bbb {RP}}^2$ -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 $\bold {PGL}(3,{\Bbb R})$ , establishing a conjecture of Hitchin.

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Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 57M05, 53A20

Suhyoung Choi
Affiliation: Department of Mathematics, College of Natural Sciences, Seoul National University, 151-742 Seoul, Korea
Email: shchoi@math.snu.ac.kr

William M. Goldman
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: wmg@math.umd.edu

DOI: 10.1090/S0273-0979-97-00711-8
PII: S 0273-0979(97)00711-8
Keywords: Real projective structure, convex real projective structure, deformation space, representation of fundamental groups, developing map, holonomy, Teichmüller, Higgs bundle, $\bf{SL}(3,\Bbb{R})$-representation variety
Received by editor(s): April 15, 1994,
Received by editor(s) in revised form: October 13, 1996
Additional Notes: Choi gratefully acknowledges partial support from GARC-KOSEF
Goldman gratefully acknowledges partial support from the National Science Foundation, the Alfred P. Sloan Foundation and the Institute for Advanced Computer Studies at the University of Maryland.
Copyright of article: Copyright 1997, American Mathematical Society

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