On the topology of ending lamination space

Gabai, David

doi:10.2140/gt.2014.18.2683

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On the topology of ending lamination space

David Gabai

Geometry & Topology 18 (2014) 2683–2745

DOI: 10.2140/gt.2014.18.2683

Abstract

We show that if $S$ is a finite-type orientable surface of genus $g$ and with $p$ punctures, where $3 g + p \geq 5$ , then $ℰ ℒ (S)$ is $(n - 1)$ –connected and $(n - 1)$ –locally connected, where $dim (P ℳ ℒ (S)) = 2 n + 1 = 6 g + 2 p - 7$ . Furthermore, if $g = 0$ , then $ℰ ℒ (S)$ is homeomorphic to the $(p - 4)$ –dimensional Nöbeling space. Finally if $n \neq 0$ , then $ℱ P ℳ ℒ (S)$ is connected.

Keywords

Nöbeling, lamination

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 20F65

References

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

Volume 18, issue 5 (2014)