The symplectic global coordinates on the moduli space of real projective structures

Journal of Differential Geometry

Volumn 53, Issue 2, 1999, Pages 359-401

  Kim, Hong Chan ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b Korea Institute for Advanced Study   (South Korea)

Author keywords

Fundamental cycle; Group cohomology; Moduli space; Real projective structure; Symplectic global coordinates; Symplectic structure

Indexed keywords

EID: 0038853062     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214425539     Document Type: Article

References (17)

1. W. Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Math., Vol. 820, Springer, Berlin, 1980.
2. M. Atiyah & R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. Roy. Soc. London Ser. A 308 (1982) 523-615.
3. M. Audin, Lectures on gauge theory and integrable systems, Gauge theory and symplectic geometry (Montreal, PQ, 1995), 1-48, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 488, Kluwer Acad. Publ., Dordrecht, 1997.
4. K. Brown, Cohomology of groups, Graduate Texts in Math. 87, Springer, Berlin, 1982.
5. C. Ehresmann, Sur les espaces localement homogenes, Enseign. Math. 35 (1937) 317-333.
6. R. Fox, The free differential calculus. I. Derivations in the group ring, Ann. of Math. 57 (1953) 547-560.
7. W. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984), 200-225.
8. W. Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 126-159.
9. W. Goldman & J. Millson The deformation theory of representations of fundamental groups of compact Kdhler manifolds, Bull. Amer. Math. Soc. (N.S.) 18 (1988) 153-158.
10. K. Guruprasad, J. Huebschmann, L. Jeffrey & A. Weinstein Group systems, groupoids, and moduli spaces of parabolic bundles, Duke Math. J. 89 (1997) 377-412.
11. H. Kim, The symplectic structure on the moduli space of real projective structures, Ph.D. dissertation, University of Maryland, 1999, 1-90.
12. N. Kuiper, On convex locally projective spaces, Convegno Internat. Geometria Differenziale, Italy, 1954, 200-213.
13. R. Lyndon, Cohomology theory of groups with one defining relation, Ann. of Math. 52 (1950) 650-665.
14. M. Raghunathan, Discrete Subgroups of Lie Groups, Springer, Berlin, 1972.
15. D. Sullivan & W. Thurston, Manifolds with canonical coordinates: Some examples, Enseign. Math. 29 (1983) 15-25.
16. A. Weil, Remark on the Cohomology of groups, Ann. of Math. 80 (1964) 149-157.
17. S. Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math. 107 (1985) 969-997.