Volume 18, issue 5 (2014)

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On the topology of ending lamination space

David Gabai

Geometry & Topology 18 (2014) 2683–2745
Abstract

We show that if $S$ is a finite-type orientable surface of genus $g$ and with $p$ punctures, where $3g+p\ge 5$, then $\mathsc{ℰ}\phantom{\rule{0.3em}{0ex}}\mathsc{ℒ}\left(S\right)$ is $\left(n-1\right)$–connected and $\left(n-1\right)$–locally connected, where $dim\left(\mathsc{P}\mathsc{ℳ}\mathsc{ℒ}\left(S\right)\right)=2n+1=6g+2p-7$. Furthermore, if $g=0$, then $\mathsc{ℰ}\mathsc{ℒ}\left(S\right)$ is homeomorphic to the $\left(p-4\right)$–dimensional Nöbeling space. Finally if $n\ne 0$, then $\mathsc{ℱ}\mathsc{P}\mathsc{ℳ}\mathsc{ℒ}\left(S\right)$ is connected.

Keywords
Nöbeling, lamination
Primary: 57M50
Secondary: 20F65
Publication
Received: 19 October 2011
Revised: 5 December 2011
Accepted: 15 July 2012
Published: 1 December 2014
Proposed: Walter Neumann
Seconded: Michael Freedman, Danny Calegari
Authors
 David Gabai Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544 USA