Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 4 (2009), 2175-2189.
Depth of pleated surfaces in toroidal cusps of hyperbolic $3$–manifolds
Let be a closed essential surface in a hyperbolic –manifold with a toroidal cusp . The depth of in is the maximal distance from points of in to the boundary of . It will be shown that if is an essential pleated surface which is not coannular to the boundary torus of then the depth of in is bounded above by a constant depending only on the genus of . The result is used to show that an immersed closed essential surface in which is not coannular to the torus boundary components of will remain essential in the Dehn filling manifold after excluding curves from each torus boundary component of , where is a constant depending only on the genus of the surface.
Algebr. Geom. Topol., Volume 9, Number 4 (2009), 2175-2189.
Received: 10 March 2009
Accepted: 21 September 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Wu, Ying-Qing. Depth of pleated surfaces in toroidal cusps of hyperbolic $3$–manifolds. Algebr. Geom. Topol. 9 (2009), no. 4, 2175--2189. doi:10.2140/agt.2009.9.2175. https://projecteuclid.org/euclid.agt/1513797080