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

Donghi Lee

Department of Mathematics, Pusan National University, San-30 Jangjeon-Dong, Geumjung-Gu, Pusan 609-735, Korea

E-mail Address: donghi@pusan.ac.kr

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and

Makoto Sakuma

Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

E-mail Address: sakuma@math.sci.hiroshima-u.ac.jp

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https://doi.org/10.1142/S021821651650067XCited by:0 (Source: Crossref)

Abstract

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

Keywords:

AMSC: 20F06, 57M25

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