Mathematics > Geometric Topology
[Submitted on 17 Apr 2011 (v1), last revised 23 Mar 2012 (this version, v2)]
Title:Characteristic submanifold theory and toroidal Dehn filling
View PDFAbstract:The exceptional Dehn filling conjecture of the second author concerning the relationship between exceptional slopes $\alpha, \beta$ on the boundary of a hyperbolic knot manifold $M$ has been verified in all cases other than small Seifert filling slopes. In this paper we verify it when $\alpha$ is a small Seifert filling slope and $\beta$ is a toroidal filling slope in the generic case where $M$ admits no punctured-torus fibre or semi-fibre, and there is no incompressible torus in $M(\beta)$ which intersects $\partial M$ in one or two components. Under these hypotheses we show that $\Delta(\alpha, \beta) \leq 5$. Our proof is based on an analysis of the relationship between the topology of $M$, the combinatorics of the intersection graph of an immersed disk or torus in $M(\alpha)$, and the two sequences of characteristic subsurfaces associated to an essential punctured torus properly embedded in $M$.
Submission history
From: Xingru Zhang [view email][v1] Sun, 17 Apr 2011 15:39:40 UTC (679 KB)
[v2] Fri, 23 Mar 2012 21:01:11 UTC (624 KB)
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