Taut foliations of torus knot complements
Vol. 14 (2007), No. 1, Page 31--67.
NAKAE, Yasuharu
Taut foliations of torus knot complements
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Abstract:
We show that for any torus knot $K(r,s)$, $|r|>s>0$, there is a family of taut foliations of the complement of $K(r,s)$, which realizes all boundary slopes in $(-\infty, 1)$ when $r>0$, or $(-1,\infty)$ when $r<0$. This theorem is proved by a construction of branched surfaces and laminations which are used in the Roberts paper~\cite{RR01a}. Applying this construction to a fibered knot ${K}'$, we also show that there exists a family of taut foliations of the complement of the cable knot $K$ of ${K}'$ which realizes all boundary slopes in $(-\infty,1)$ or $(-1,\infty)$. Further, we partially extend the theorem of Roberts to a link case.
Mathematics Subject Classification (2000): Primary 57M25; Secondary 57R30
Mathematical Reviews Number: MR2320384
Received: 2005-09-14
