Almost filling laminations and the connectivity of ending lamination space

Gabai, David

doi:10.2140/gt.2009.13.1017

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Almost filling laminations and the connectivity of ending lamination space

David Gabai

Geometry & Topology 13 (2009) 1017–1041

DOI: 10.2140/gt.2009.13.1017

Abstract

We show that if $S$ is a finite type orientable surface of negative Euler characteristic which is not the $3$ –holed sphere, $4$ –holed sphere or $1$ –holed torus, then the space of ending laminations of $S$ is path connected, locally path connected and cyclic.

Keywords

lamination, connectivity, curve complex, surface

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 57R30, 51M10, 20F65

References

Publication

Received: 5 September 2008

Revised: 3 January 2009

Accepted: 4 December 2008

Published: 21 January 2009

Proposed: Benson Farb

Seconded: Jean-Pierre Otal, Tobias Colding

Authors

David Gabai
Department of Mathematics Princeton University Princeton, NJ 08544 USA

Volume 13, issue 2 (2009)