The geometry of the Eisenstein-Picard modular group

Duke Mathematical Journal

Volumn 131, Issue 2, 2006, Pages 249-289

  Falbel, Elisha ^a   Parker, John R ^b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33244463074     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-06-13123-X     Document Type: Article

References (22)

1. [A] R. ALEZAIS, Sur une classe de fonctions hyperfuchsiennes et sur certaines substitutions linéaires qui s'y rapportent, Ann. Sci. École Norm. Sup. (3) 19 (1902), 261-323. MR 1509013
2. [D] M. DERAUX, Dirichlet domains for the Mostow lattices, to appear in Experiment. Math., preprint, 2005, http://www-fovrier.ujf-grenoble.fr/~deraux/ recherche/
3. [DFP] M. DERAUX, E. FALBEL, and J. PAUPERT, New constructions of fundamental polyhedra in complex hyperbolic space, Acta Math. 194 (2005), 155-201.
4. [EP] D. B. A. EPSTEIN and C. PETRONIO, An exposition of Poincaré's polyhedron theorem, Enseign. Math. (2) 40 (1994), 113-170. MR 1279064
5. [FK] E. FALBEL and P.-V. KOSELEFF, Rigidity and flexibility of triangle groups in complex hyperbolic geometry, Topology 41 (2002), 767-786. MR 1905838
6. [FP] E. FALBEL and J. R. PARKER, The moduli space of the modular group, Invent. Math. 152 (2003), 57-88. MR 1965360
7. [OR] H. GARLAND and M. S. RAGHUNATHAN, Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups, Ann. of Math. (2) 92 (1970), 279-326. MR 0267041
8. [G] G. GIRAUD, Sur certaines fonctions automorphes de deux variables, Ann. Sci. École Norm. Sup. (3) 38 (1921), 43-164. MR 1509233
9. [Go] W. M. GOLDMAN, Complex Hyperbolic Geometry, Oxford Math. Monogr., Oxford Univ. Press, New York, 1999. MR 1695450
10. [H1] R.-P. HOLZAPFEL, Invariants of arithmetic ball quotient surfaces, Math. Nachr. 103 (1981), 117-153. MR0653917
11. [H2] _, Geometry and Arithmetic around Euler Partial Differential Equations, Math. Appl. 11, Reidel, Dordrecht, 1986. MR 0867406
12. [H3] _, "Symplectic representation of a braid group on 3-sheeted covers of the Riemann sphere" in Conference on Geometry and Mathematical Physics (Zlatograd, Bulgaria, 1995), Serdica Math. J. 23, Bulgarian Acad. Sci., Sofia, 1997, 143-164. MR 1627589
13. [KR] A. KORÁNYI and H. M. REIMANN, Quasiconformal mappings on the Heisenberg group, Invent. Math. 80 (1985), 309-338. MR 0788413
14. [L] J. LEHNER, A Short Course in Automorphic Functions, Holt, Rinehart and Winston, New York, 1966. MR 0201637
15. [Li] R. A. LIVNÉ, On certain covers of the universal elliptic curve, Ph.D. dissertation, Harvard University, Cambridge, Mass., 1981.
16. [M] G. D. MOSTOW, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86 (1980), 171-276. MR 0586876
17. [P1] J. R. PARKER, On the volumes of cusped, complex hyperbolic manifolds and orbifolds, Duke Math. J. 94 (1998), 433-464. MR 1639519
18. [P2] _, Cone metrics on the sphere and Livné's lattices, to appear in Acta Math., preprint, 2005, http://fourier.dur.ac.uk:8000/~rdmaOjrp/ #preprints
19. [Pi1] E. PICARD, Sur des fonctions de deux variables indépendentes analogues aux fonctions modulaires, Acta Math. 2 (1883), 114-135.
20. [Pi2] _, Sur des formes quadratiques ternaires indéfinies indéterminées conjuguées et sur les fonctions hyperfuchsiennes correspondantes, Acta Math. 5 (1884), 121-182.
21. [S] G. P. SCOTT, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487. MR 0705527
22. [Sw] R. G. SWAN, Generators and relations for certain special linear groups, Adv. Math. 6 (1971), 1-77. MR 0284516