Depth of pleated surfaces in toroidal cusps of hyperbolic 3–manifolds

Wu, Ying-Qing¹

¹Department of Mathematics, University of Iowa, Iowa City, IA 52242

Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 2175-2189

Résumé

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.

Détail

DOI : 10.2140/agt.2009.9.2175

Keywords: pleated surface, hyperbolic manifold, immersed surface, Dehn surgery

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