Volume 9, issue 4 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Depth of pleated surfaces in toroidal cusps of hyperbolic $3$–manifolds

Ying-Qing Wu

Algebraic & Geometric Topology 9 (2009) 2175–2189

Let F be a closed essential surface in a hyperbolic 3–manifold M with a toroidal cusp N. The depth of F in N is the maximal distance from points of F in N to the boundary of N. It will be shown that if F is an essential pleated surface which is not coannular to the boundary torus of N then the depth of F in N is bounded above by a constant depending only on the genus of F. The result is used to show that an immersed closed essential surface in M which is not coannular to the torus boundary components of M will remain essential in the Dehn filling manifold M(γ) after excluding Cg curves from each torus boundary component of M, where Cg is a constant depending only on the genus g of the surface.

pleated surface, hyperbolic manifold, immersed surface, Dehn surgery
Mathematical Subject Classification 2000
Primary: 57N10
Received: 10 March 2009
Accepted: 21 September 2009
Published: 21 October 2009
Ying-Qing Wu
Department of Mathematics
University of Iowa
Iowa City, IA 52242