Dehn fillings on a two torus boundary components 3-manifold
type: Item
instance of: scholarly article
title: Dehn fillings on a two torus boundary components 3-manifold
zbMATH Open document ID: 1025.57029
author: Elsa Mayrand
published in: Osaka Journal of Mathematics
publication date: 2002-01-01T00:00:00Z
review text: Let \(X\) be a 3-manifold with two incompressible torus boundary components: \(\partial X= T_1\cup T_2\). Suppose further that \(P\) and \(Q\) are planar surfaces properly embedded in \(X\). By analysing the possible intersections of \(P\) and \(Q\) in \(X\), the author attempts to extend to two torus boundary components the important analysis carried out by Gordon and Luecke for one torus boundary component. That is, let \(\alpha_i\) be a curve parallel to the curves of intersection of \(P\) with \(T_i\) and let \(\beta_i\) be a curve parallel to the curves of intersection of \(Q\) with \(T_i\). Then one seeks upper bounds on the geometric intersection numbers of \(\alpha_i\) with \(\beta_i\) in \(T_i\). Subject to certain nontriviality conditions, the author obtains such upper bounds for at least one of the pairs \((\alpha_i,\beta_1)\) (distance between boundary slopes).
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N12
zbMATH DE Number: 1874586
zbMATH Keywords: Dehn surgery
zbMATH Keywords: Dehn fillings
zbMATH Keywords: boundary slopes
reviewed by: James W. Cannon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1874586