The monodromy groups of Schwarzian equations on closed Riemann surfaces

Annals of Mathematics

Volumn 151, Issue 2, 2000, Pages 625-704

  Gallo, Daniel ^a   Kapovich, Michael ^b   Marden, Albert ^c  

^a ST JOHN'S UNIVERSITY   (United States)

^b UNIVERSITY OF UTAH   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034392014     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121044     Document Type: Article

References (51)

1. D. V. Anosov and A. A. Bolibruch, The Riemann-Hilbert Problem, Aspects of Math. 32, Friedr, Vieweg, Braunschweig, 1994.
2. M. Atiyah, Complex analytic connections in fibre bundles, Trans. A.M.S. 85 (1957), 181-207.
3. C. Banica and O. Stanasila, Algebraic Methods in the Global Theory of Complex Spaces, John Wiley & Sons, New York, 1976.
4. A. Beauville, Complex Algebraic Surfaces, London Math. Society Student Texts 34, Cambridge Univ. Press, Cambridge, 1996.
5. V. Benyash-Krivetz, V. I. Chernousov, and A. S. Rapinchuk, Representation varieties of the fundamental groups of compact orientable surfaces, Israel J. Math. 93 (1996), 29-71.
6. R. Canary, D. B. A. Epstein, and P. Green, Notes on notes of Thurston, in Analytical and Geometric Aspects of Hyperbolic Space, London Math. Society Lecture Notes 111 (1987), 3-92.
7. S. Choi and H. Lee, Geometric structures on manifolds and holonomy-invariant metrics, Forum Math. 9 (1997), 247-256.
8. V. Chuckrow, On Schottky groups with application to kleinian groups, Ann. of Math. 88 (1968), 47-61.
9. C. Earle, On variation of projective structures, in Riemann Surfaces and Related Topics (I. Kra and B. Maskit, eds.), Ann. of Math. Studies 97, 87-99, Princeton Univ. Press, Princeton, NJ, 1981.
10. G. Faltings, Real projective structures on Riemann surfaces, Compositio Math. 48 (1983), 223-269.
11. D. Gallo, Prescribed holonomy for projective structures on compact surfaces, Bull. A.M.S. 20 (1989), 31-34.
12. _, The topology of real projective structures, in Lipa's Legacy (New York, 1995), 253-260, Contemp. Math. 211, A.M.S., Providence, RI, 1997.
13. _, The topology of real projective structures, in Lipa's Legacy (New York, 1995), 253-260, Contemp. Math. 211, A.M.S., Providence, RI, 1997.
14. D. Gallo, W. Goldman, and M. Porter, Projective structures with monodromy in PSL(2, ℙ.), preprint, 1987.
15. W. Goldman, Projective structures with Fuchsian holonomy, J. Differential Geom. 25 (1987), 297-326.
16. _, Topological components of spaces of representations, Invent. Math. 93 (1988), 557-607.
17. L. Greenberg, Discrete subgroups of the Lorentz group, Math. Scand. 10 (1962), 85-107.
18. R. Gunning, Special coordinate coverings of Riemann surfaces, Math. Ann. 170 (1967), 67-86.
19. _, Lectures on Vector Bundles over Riemann Surfaces, Princeton Univ. Press, Princeton, NJ, 1967.
20. _, Affine and projective structures on Riemann surfaces, in Riemann Surfaces and Related Topics (I. Kra and B. Maskit, eds.), Ann. of Math. Studies 97, Princeton Univ. Press, Princeton, NJ, 1981.
21. _, Introduction to Holomorphic Function of Several Variables, Vol. II: Local Theory, The Wadsworth & Brooks/Cole Math. Series, Wadsworth & Brooks/Cole Adv. Books and Software, Monterey, CA, 1990.
22. N. S. Hawley and M. Schiffer, Half-order differentials on Riemann surfaces, Acta Math. 115 (1966), 199-236.
23. D. Hejhal, Monodromy groups and linearly polymorphic functions, Acta Math. 135 (1975), 1-55.
24. _, Monodromy groups for higher-order differential equations, Bull. A.M.S. 81 (1975), 590-592.
25. _, Monodromy groups and Poincaré series, Bull. A.M.S. 84 (1978), 339-376.
26. N. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), 59-126.
27. K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida, From Gauss to Painlevé, Aspects of Math. E16, Friedr. Vieweg & Sohn, Braunschweig, 1991.
28. T. Jorgensen and P. Klein, Algebraic convergence of finitely generated Kleinian groups, Quart. J. Math. 33 (1982), 325-335.
29. M. Kapovich, On monodromy of complex projective structures, Invent. Math. 119 (1995), 243-265.
30. I. Kra, Deformations of Fuchsian groups I, Duke Math. J. 36 (1969) 537-546
31. _, Deformation of Fuchsian groups, II, Duke Math. J. 38 (1971), 499-508.
32. N. J. Kuiper, On compact conformally Euclidean spaces of dimension > 2, Ann. of Math. 52 (1950), 478-490.
33. R. Kulkarni and U. Pinkall, Uniformization of geometric structures with applications to conformal geometry, in Differential Geometry Peñíscola 1985, 190-209, Lecture Notes in Math. 1209, Springer-Verlag, New York, 1986.
34. H. Lange, Zur klassifikation von Regelmannigfaltigkeiten, Math. Ann. 262 (1983), 447-459.
35. Jun Li, The space of surface group representations, Manuscripta Math. 78 (1993), 223-243.
36. F. Luo, Monodromy groups of projective structures on punctured surfaces, Invent. Math. 111 (1993), 541-555.
37. R. Mandelbaum, Branched structures on Riemann surfaces, Trans. A.M.S. 163 (1972), 261-275.
38. _, Branched structures and affine and projective bundles on Riemann surfaces, Trans. A.M.S. 183 (1973), 37-58.
39. _, Unstable bundles and branched structures on Riemann surfaces, Math. Ann. 214 (1975), 49-59.
40. B. Maskit, On a class of Kleinian groups, Ann. Acad. Sci. Fenn. 442 (1969), 1-8.
41. _, Kleinian Groups, Springer-Verlag, New York, 1988.
42. P. Melvin, 2-sphere bundles over compact surfaces, Proc. A.M.S. 92 (1984), 567-572.
43. M. Narasimhan and C. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), 540-567.
44. H. Poincaré, Sur les groups des équations linéaires, Acta Math. 4 (1884), 201-312.
45. R. Rubinsztein, personal communication, Uppsala Univ., 1996.
46. Y. Sibuya, Linear Differential Equations in the Complex Domain: Problems of Analytic Continuation, Transl. of Math. Monographs 82, A.M.S., Providence, RI, 1990.
47. 1-structures on surfaces with prescribed real holonomy, Math. Ann. 300 (1994), 649-667.
48. H. Tanigawa, Divergence of projective structures and lengths of measured laminations, Duke Math. J. 98 (1999), 209-215.
49. A. Weil, Généralisation des fonctions abeliennes, J. de Math. Pure et Appl. (IX) 17 (1938), 47-87.
50. M. Yoshida, Fuchsian Differential Equations, Aspects of Math. E11, Friedr. Vieweg & Sohn, Braunschweig, 1987.
51. H. Zieschang, Über einfache Kurven auf Vollbrezeln, Abh. Math. Sem. Univ. Hamburg 25 (1962), 231-250.