### Abstract

We show that if S is a finite-type orientable surface of genus g and with p punctures where 3g+p≥5, then EL(S)is (n-1)-connected and (n-1)-locally connected, where dim (PML(S)) = 2n+1=6g+2p-7. Furthermore, if g =0, then EL(S) is homeomorphic to the (p-4)-dimensional Nöbeling space. Finally if n ≠ 0, then FPML(S) is connected.

Original language | English (US) |
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Pages (from-to) | 2683-2745 |

Number of pages | 63 |

Journal | Geometry and Topology |

Volume | 18 |

Issue number | 5 |

DOIs | |

State | Published - Dec 1 2014 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

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## Cite this

Gabai, D. (2014). On the topology of ending lamination space.

*Geometry and Topology*,*18*(5), 2683-2745. https://doi.org/10.2140/gt.2014.18.2683