Duke Mathematical Journal

Connectivity of the space of ending laminations

Christopher J. Leininger and Saul Schleimer

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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

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Duke Math. J., Volume 150, Number 3 (2009), 533-575.

First available in Project Euclid: 27 November 2009

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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

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