Duke Mathematical Journal
- Duke Math. J.
- Volume 150, Number 3 (2009), 533-575.
Connectivity of the space of ending laminations
We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E. Klarreich [28, Theorem 1.3] implies that this space is homeomorphic to the Gromov boundary of the complex of curves. It follows that the boundary of the complex of curves is connected in these cases, answering the conjecture of P. Storm. Other applications include the rigidity of the complex of curves and connectivity of spaces of degenerate Kleinian groups
Duke Math. J., Volume 150, Number 3 (2009), 533-575.
First available in Project Euclid: 27 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Leininger, Christopher J.; Schleimer, Saul. Connectivity of the space of ending laminations. Duke Math. J. 150 (2009), no. 3, 533--575. doi:10.1215/00127094-2009-059. https://projecteuclid.org/euclid.dmj/1259332508