SIMPLE LOOPS ON 2-BRIDGE SPHERES IN HECKOID ORBIFOLDS FOR THE TRIVIAL KNOT
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In this paper, we give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.
Abstract
In this paper, we give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.
참고문헌 (15)
- M. Boileau, "Three-dimensional orbifolds and their geometric structures", Panoramas et Syntheses, 15 (2003), Societe Mathematique de France
- M. Boileau, "Geometrization of 3-orbifolds of cyclic type, Appendix A by Michael Heusener and Porti", Asterisque, (272) (2001)
- C. Gordon, "Problems", Workshop on Heegaard Splittings, 12, pp.401~411 (2007), Geom. Topol. Monogr.
- E. Hecke, "Uber die Bestimung Dirichletscher Reihen durch ihre Funktionalgleichung", Math. Ann., 112, pp.664~699 (1936)
- D. Lee, "Simple loops on 2-bridge spheres in 2-bridge link complements", Electron. Res. Announc. Math. Sci., 18, pp.97~111 (2011)
- D. Lee, "Epimorphisms between 2-bridge link groups: homotopically trivial simple loops on 2-bridge spheres", Proc. London Math. Soc., 104, pp.359~386 (2012)
- D. Lee, "Simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links", Electron. Res. Announc. Math. Sci., 19, pp.97~111 (2012)
- D. Lee, "Epimorphisms from 2-bridge link groups onto Heckoid groups (I)", Hiroshima Math. J., 43, pp.239~264 (2013)
- D. Lee, "Epimorphisms from 2-bridge link groups onto Heckoid groups (II)", Hiroshima Math. J., 43, pp.265~284 (2013)
- D. Lee, "Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (I)", arXiv:1402.6870, ~
- D. Lee, "Homotopically equivalent simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links (II)", arXiv:1402.6873, ~
- R. C. Lyndon, "Combinatorial group theory" (1977), Springer-Verlag
- B. B. Newman, "Some results on one-relator groups", Bull. Amer. Math. Soc., 74, pp.568~571 (1968)
- R. Riley, "Parabolic representations of knot groups, I", Proc. London Math. Soc., 24, pp.217~242 (1972)
- R. Riley, "Algebra for Heckoid groups", Trans. Amer. Math. Soc., 334, pp.389~409 (1992)