Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (I) |
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| Authors: | Donghi Lee Makoto Sakuma |
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| Affiliation: | 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: | In this paper and its two sequels, we 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. This paper treats the case when the 2-bridge link is a ((2,p)) -torus link, where more cases of homotopy arise, and its sequels will treat the remaining cases. |
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