CONVEX REAL PROJECTIVE-STRUCTURES ON CLOSED SURFACES ARE CLOSED

Authors
CHOI S GOLDMAN WM
Citation
S. Choi et Wm. Goldman, CONVEX REAL PROJECTIVE-STRUCTURES ON CLOSED SURFACES ARE CLOSED, Proceedings of the American Mathematical Society, 118(2), 1993, pp. 657-661
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
118
Issue
2
Year of publication
1993
Pages
657 - 661
Database
ISI
SICI code
0002-9939(1993)118:2<657:CRPOCS>2.0.ZU;2-#
Abstract
The deformation space c(SIGMA) of convex RP2- structures on a closed s urface SIGMA with CHI(SIGMA) < 0 is closed in the space Hom(pi, SL(3, R))/SL(3, R) of equivalence classes of representations pi1(SIGMA) --> SL(3, R). Using this fact, we prove Hitchin's conjecture that the cont ractible ''Teichmuller component'' (Lie groups and Teichmuller space, preprint) of Hom(pi, SL(3, R))/SL(3, R) precisely equals c(SIGMA).