Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (III) |
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Authors: | Donghi Lee Makoto Sakuma |
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Institution: | 1. Department of Mathematics, Pusan National University, Pusan, 609-735, Republic of Korea 2. Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan
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Abstract: | This is the last of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series treated the case of the 2-bridge torus links, and the second paper treated the case of 2-bridge links of slope \(n/(2n+1)\) and \((n+1)/(3n+2)\) , where \(n \ge 2\) is an arbitrary integer. In this paper, we first treat the case of 2-bridge links of slope \(n/(mn+1)\) and \((n+1)/((m+1)n+m)\) , where \(m \ge 3\) is an arbitrary integer, and then treat the remaining cases by induction. |
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