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### Connectivity of the space of ending laminations

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Leininger, Christopher J. and Schleimer, Saul.
(2009)
*Connectivity of the space of ending laminations.*
Duke Mathematical Journal, Vol.150
(No.3).
pp. 533-575.
ISSN 0012-7094

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Official URL: http://dx.doi.org/10.1215/00127094-2009-059

## 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.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Surfaces, Algebraic, Hyperbolic spaces, Curves, Algebraic |

Journal or Publication Title: | Duke Mathematical Journal |

Publisher: | Duke University Press |

ISSN: | 0012-7094 |

Date: | 2009 |

Volume: | Vol.150 |

Number: | No.3 |

Page Range: | pp. 533-575 |

Identification Number: | 10.1215/00127094-2009-059 |

Status: | Peer Reviewed |

Access rights to Published version: | Open Access |

Funder: | National Science Foundation (U.S.) (NSF) |

Grant number: | DMS-0603881 (NSF), DMS-0508971 (NSF) |

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URI: | http://wrap.warwick.ac.uk/id/eprint/3138 |

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