Geometry & Topology

On the topology of ending lamination space

David Gabai

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We show that if S is a finite-type orientable surface of genus g and with p punctures, where 3g+p5, then (S) is (n1)–connected and (n1)–locally connected, where dim(P(S))=2n+1=6g+2p7. Furthermore, if g=0, then (S) is homeomorphic to the (p4)–dimensional Nöbeling space. Finally if n0, then P(S) is connected.

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Nöbeling lamination


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

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