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 5, then (S) is (n 1)–connected and (n 1)–locally connected, where dim(P(S)) = 2n + 1 = 6g + 2p 7. Furthermore, if g = 0, then (S) is homeomorphic to the (p 4)–dimensional Nöbeling space. Finally if n0, then P(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