TY - JOUR AU - 조상범 DA - 2012/12 PY - 2012 UR - https://www.jstage.jst.go.jp/article/tmj/64/4/64_469/_article/-char/en UR - http://hdl.handle.net/20.500.11754/50828 AB - For a genus-1 1-bridge knot in $S^3$, that is, a $(1,1)$-knot, a middle tunnel is a tunnel that is not an upper or lower tunnel for some $(1,1)$-position. Most torus knots have a middle tunnel, and non-torus-knot examples were obtained by Goda, Hayashi, and Ishihara. We generalize their construction and calculate the slope invariants for the resulting middle tunnels. In particular, we obtain the slope sequence of the original example of Goda, Hayashi, and Ishihara PB - Mathematical Institute of Tohoku University KW - Key words and phrases KW - Knot KW - tunnel KW - (1,1) KW - torus knot. TI - MIDDLE TUNNELS BY SPLITTING IS - 4 VL - 64 DO - 10.2748/tmj/1356038975 T2 - TOHOKU MATHEMATICAL JOURNAL ER -