Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II)

Details Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II) Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II)

2011-03-04

arxiv.org/abs/1103.0856v3

Mathematics

Group Theory

51 pages, 25 figures; Section 8 added, references updated and added

Scientific paper

This is the second of series of papers which give the 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 [4] treated the case of the 2-bridge torus links. In this paper, we treat the case of 2-bridge links of slope $n/(2n+1)$ and $(n+1)/(3n+2)$, where $n \ge 2$ is an arbitrary integer.

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