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P2-reducing and toroidal Dehn fillings

Published online by Cambridge University Press:  01 May 2003

GYO TAEK JIN ,
SANGYOP LEE ,
SEUNGSANG OH  and
MASAKAZU TERAGAITO
GYO TAEK JIN
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea. e-mail: [email protected]
SANGYOP LEE
Affiliation:
School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu Seoul 130-012, Korea. e-mail: [email protected]
SEUNGSANG OH
Affiliation:
Department of Mathematics, Chonbuk National University, Chonju, Chonbuk 561-756, Korea. e-mail: [email protected]
MASAKAZU TERAGAITO
Affiliation:
Department of Mathematics and Mathematics Education, Hiroshima University, Kagamiyama 1-1-1, Higashi-hiroshima 739-8524, Japan. e-mail: [email protected]
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Abstract

Let M be a compact, connected, orientable 3-manifold with a torus boundary component $\partial_{0}M$. A slope on $\partial_{0}M$ is the isotopy class of an unoriented essential simple loop. For a slope r, the manifold obtained from M by r-Dehn filling is M(r) = M$\cup$Vr, where Vr is a solid torus glued to M along $\partial_{0}M$ in such a way that r bounds a meridian disc in Vr. If r and s are two slopes on $\partial_{0}M$, then $\Delta$(r, s) denotes their minimal geometric intersection number.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 134 , Issue 2 , March 2003 , pp. 271 - 288
Copyright
2003 Cambridge Philosophical Society

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