2009
DOI: 10.2140/agt.2009.9.2175
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Depth of pleated surfaces in toroidal cusps of hyperbolic 3–manifolds

Abstract: 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 w… Show more

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“…However, for hyperbolic M such a surface F can compress in at most finitely many Dehn fillings M (γ); see [1]. In fact in [18], it is shown that there is a bound on the number of fillings in which F can compress depending only on the genus of F , and not on the manifold M . Wu has asked whether there is any universal bound, independent of F , for this number (Question 6.6 in [17]).…”
Section: Introductionmentioning
confidence: 99%
“…However, for hyperbolic M such a surface F can compress in at most finitely many Dehn fillings M (γ); see [1]. In fact in [18], it is shown that there is a bound on the number of fillings in which F can compress depending only on the genus of F , and not on the manifold M . Wu has asked whether there is any universal bound, independent of F , for this number (Question 6.6 in [17]).…”
Section: Introductionmentioning
confidence: 99%