Geometry & Topology

On the topology of ending lamination space

David Gabai

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.

Article information

Source
Geom. Topol., Volume 18, Number 5 (2014), 2683-2745.

Dates
Received: 19 October 2011
Revised: 5 December 2011
Accepted: 15 July 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732882

Digital Object Identifier
doi:10.2140/gt.2014.18.2683

Mathematical Reviews number (MathSciNet)
MR3285223

Zentralblatt MATH identifier
1307.57012

Keywords
Nöbeling lamination

Citation

Gabai, David. On the topology of ending lamination space. Geom. Topol. 18 (2014), no. 5, 2683--2745. doi:10.2140/gt.2014.18.2683. https://projecteuclid.org/euclid.gt/1513732882

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