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arXiv · 1402.6870

Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (I)

Donghi Lee·Makoto Sakuma
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Abstract

In this paper and its sequel, we give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even Heckoid orbifold for a 2-bridge link to be peripheral or torsion in the orbifold. This paper treats the case when the 2-bridge link is a $(2,p)$-torus link, and its sequel will treat the remaining cases.

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Donghi Lee, Makoto Sakuma. 2014-02-27. Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (I). https://arxiv.org/abs/1402.6870

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