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 タイトル: Taut foliations of torus knot complements 著者: Nakae, Yasuharu 発行日: 2007年3月20日 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 14 (2007), No. 1, Page 31-67 抄録: 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. URI: http://hdl.handle.net/2261/20681 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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