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Toroidal Dehn Fillings on Hyperbolic 3-Manifolds
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Artikel-Nr:
9781470405151
Einband:
PDF
Seiten:
140
Autor:
Cameron McA Gordon
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:
The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T_0$, and $r,s$ are two slopes on $T_0$ with $Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M_i$, or obtained from $M_1, M_2, M_3$ or $M_{14}$ by attaching a solid torus to $partial M_i - T_0$. All the manifolds $M_i$ are hyperbolic, and the authors show that only the first three can be embedded into $S^3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S^3$ admitting two toroidal surgeries with distance at least $4$.
The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T_0$, and $r,s$ are two slopes on $T_0$ with $Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M_i$, or obtained from $M_1, M_2, M_3$ or $M_{14}$ by attaching a solid torus to $partial M_i - T_0$. All the manifolds $M_i$ are hyperbolic, and the authors show that only the first three can be embedded into $S^3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S^3$ admitting two toroidal surgeries with distance at least $4$.