Location of Repository

Connectivity of the space of ending laminations

By Christopher J. Leininger and Saul Schleimer


We prove that for any closed surface of genus at least four, and any punctured surface\ud of genus at least two, the space of ending laminations is connected. A theorem of E.\ud Klarreich [28, Theorem 1.3] implies that this space is homeomorphic to the Gromov\ud boundary of the complex of curves. It follows that the boundary of the complex of curves\ud is connected in these cases, answering the conjecture of P. Storm. Other applications\ud include the rigidity of the complex of curves and connectivity of spaces of degenerate\ud Kleinian groups

Topics: QA
Publisher: Duke University Press
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:3138

Suggested articles



  1. (1996). A covering theorem for hyperbolic 3-manifolds and its applications, doi
  2. (1969). A fibre bundle description of Teichm¨ uller theory,J .
  3. (2009). Almost filling laminations and the connectivity of ending lamination space, doi
  4. (1986). Bouts des vari´ et´ es hyperboliques de dimension 3, doi
  5. CANARY,a n dY. N. MINSKY, The classification of Kleinian surface groups, II: The ending lamination conjecture, doi
  6. (1998). Cannon-Thurston maps for hyperbolic group extensions, doi
  7. (1986). Compact submanifolds of 3-manifolds with boundary,Q u a r t doi
  8. (1973). Compact submanifolds of 3-manifolds, doi
  9. (2000). Continuity of Thurston’s length function, doi
  10. (2002). Convex cocompact subgroups of mapping class groups, doi
  11. (2000). Cores of hyperbolic 3-manifolds and limits of Kleinian groups, doi
  12. Curve complexes with connected boundary are rigid, doi
  13. (2006). Curve complexes, surfaces and 3-manifolds” doi
  14. (1984). EPSTEIN,a n dP. GREEN, “Notes on notes of Thurston” in Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham,
  15. (1977). Generators for the mapping class group” in Topology of Low-Dimensional Manifolds (Chelwood Gate, doi
  16. (1999). Geometry of the complex of curves, doi
  17. Hyperbolic structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle, preprint, arXiv:math/9801045v1 [math.GT]
  18. (2006). Intersection numbers and the hyperbolicity of the curve complex,J . doi
  19. LEININGER,a n dS. SCHLEIMER, Trees and mapping class groups, doi
  20. (1974). Links, and Mapping Class Groups, doi
  21. (1969). Mapping class groups and their relationship to braid groups, doi
  22. (2003). MASUR,a n dA. ZORICH, Moduli spaces of abelian differentials: The principal boundary, counting problems, and the Siegel-Veech constants, doi
  23. (1986). MASUR,a n dJ. SMILLIE, Ergodicity of billiard flows and quadratic differentials, doi
  24. MJ,a n dS. SCHLEIMER, The universal Cannon-Thurston map and the boundary of the curve complex, preprint, doi
  25. (1989). On Ahlfors’ finiteness theorem,A d v .M a t h .76 doi
  26. (2004). On the density of geometrically finite Kleinian groups, doi
  27. (1979). Quadratic differentials and foliations, doi
  28. (2004). Questions in geometric group theory, preprint,
  29. (2008). Shadows of mapping class groups: Capturing convex cocompactness, doi
  30. (1960). Simultaneous uniformization, doi
  31. (1973). spaces over Teichm¨ uller spaces, doi
  32. (1992). Subgroups of Teichm¨ uller Modular Groups, revised by the author, trans. by
  33. (1987). Teichm¨ uller Theory and Quadratic Differentials,
  34. (1999). The boundary at infinity of the curve complex and the relative Teichm¨ uller space, preprint,
  35. The classification of Kleinian surface groups, I: Models and bounds, doi
  36. (1979). The geometry and topology of 3-manifolds, Princeton lecture notes, doi
  37. (1984). The heights theorem for quadratic differentials on Riemann surfaces, doi
  38. (2001). The Hyperbolization Theorem for Fibered 3-Manifolds, translated from the 1996 French original by
  39. (2003). Train track expansions of measured foliations,
  40. (2006). Train tracks and the Gromov boundary of the complex of curves” doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.