2021-11-29T04:01:00Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000401092021-03-01T21:09:09ZTaut foliations of torus knot complementsNakae, Yasuharu138683415application/pdfWe 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.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2007-03-20application/pdfJournal of mathematical sciences, the University of Tokyo1143167AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40109/files/jms140102.pdfeng