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

2014/02/27 by Donghi Lee, Lee, Donghi, Makoto Sakuma +1
Mathematics · #20F06 #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F06 #msc:57M25

paper · pdf · doi:10.48550/arxiv.1402.6873

25 pages, 6 figures

arxiv created 2014/05/06 · arxiv updated 2014/05/07

Abstract

In this paper and its prequel, 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. The prequel treated the case when the 2-bridge link is a (2,p)-torus link, and this paper treats the remaining cases.

Related

• Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (I)
• Simple loops on 2-bridge spheres in Heckoid orbifolds for the trivial knot
• Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (I)
• Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (III)
• Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II)