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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convex real projective structures on closed surfaces are closed
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by Suhyoung Choi and William M. Goldman PDF
Proc. Amer. Math. Soc. 118 (1993), 657-661 Request permission

Abstract:

The deformation space $\mathfrak {C}(\Sigma )$ of convex $\mathbb {R}{{\mathbf {P}}^2}$-structures on a closed surface $\Sigma$ with $\chi (\Sigma ) < 0$ is closed in the space $\operatorname {Hom} (\pi ,\operatorname {SL} (3,\mathbb {R}))/\operatorname {SL} (3,\mathbb {R})$ of equivalence classes of representations ${\pi _1}(\Sigma ) \to \operatorname {SL} (3,\mathbb {R})$. Using this fact, we prove Hitchin’s conjecture that the contractible "Teichmüller component" (Lie groups and Teichmüller space, preprint) of $\operatorname {Hom} (\pi ,\operatorname {SL} (3,\mathbb {R}))/\operatorname {SL} (3,\mathbb {R})$ precisely equals $\mathfrak {C}(\Sigma )$.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 657-661
  • MSC: Primary 57M50; Secondary 14P05, 53C15, 58D27
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1145415-8
  • MathSciNet review: 1145415