The first Betti number of the smallest closed hyperbolic 3-manifold

Topology

Volumn 37, Issue 4, 1998, Pages 805-849

  Culler, Marc ^a   Hersonsky, Sa'ar ^a   Shalen, Peter B ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032085614     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-9383(97)00055-4     Document Type: Article

References (15)

1. 1. Anderson, J. W., Canary, R., Culler, M. and Shalen, P. B., Free kleinian groups and volumes of hyperbolic 3-manifolds, Journal of Differential Geometry (to appear).
2. 2. Beardon, A. F., The geometry of discrete groups. Springer, Berlin, 1983.
3. 3. Benedetti, R. and Petronio, C., Lectures on Hyperbolic Geometry. Springer, Berlin, 1992.
4. 4. Böröczky, K., Packing of spheres in spaces of constant curvature. Acta Mathematica Academy of Science Hungary, 1978, 32, 243-261.
5. 5. Canary, R. D., Ends of hyperbolic 3-manifolds. Journal of the American Mathematical Soceity, 1993, 6, 1-35.
6. 6. Culler, M. and Shalen, P. B., Paradoxical decompositions, 2-generator Kleinian groups, and volumes of hyperbolic 3-manifolds. Journal of the American Mathematical Soceity, 1992, 5, 231-288.
7. 7. Culler, M. and Shalen, P. B., Hyperbolic volume and mod p homology. Commentarii Mathematici Helvetici, 1993, 68, 494-509.
8. 8. Culler, M. and Shalen, P. B., Volumes of hyperbolic Haken manifolds, I. Inventionnes Mathematicae, 1994, 118, 285-329.
9. 9. Culler, M. and Shalen, P. B., The volume of a hyperbolic 3-manifold with Betti number 2. Proceedings of the American Mathematical Society, 1994, 120, 1281-1288.
10. 10. Douady, A., L'espace de Teichmülle:-. In Travaux de Thurston, Astérisque, Vol. 66-67, pp. 127-137. Société Mathématique de France, 1984.
11. 11. Epstein, D. B. A. and Marden, A., Convex hulls in hyperbolic spaces, a theorem of Sullivan, and measured pleated surfaces. In: Analytical and Geometrical Aspects of Hyperbolic Spaces, ed. D. B. A. Epstein, LMS Lecture Note Series, Vol. 111. Cambridge University Press, Cambridge, 1987, pp. 113-253.
12. 12. Marden, A., The geometry of finitely generated Kleinian groups. Annals of Mathematics, (2) 1974,99, 383-462.
13. 13. Meyerhoff, R., Sphere-packing and volume in hyperbolic 3-space. Commentarii Mathematici Helvetici, 1986, 61, 271-278.
14. 14. O'Neill, B., Elementary Differential Geometry. Academic Press, New York, 1966,
15. 15. Weeks, J., Hyperbolic structures on three-manifolds, Thesis, Princeton University, 1985.