## Duke Mathematical Journal

### Connectivity of the space of ending laminations

#### Abstract

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

#### Article information

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

Dates
First available in Project Euclid: 27 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1259332508

Digital Object Identifier
doi:10.1215/00127094-2009-059

Mathematical Reviews number (MathSciNet)
MR2582104

Zentralblatt MATH identifier
1190.57013

#### Citation

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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