# zbMATH — the first resource for mathematics

Epimorphisms from 2-bridge link groups onto Heckoid groups. II. (English) Zbl 1301.57007
Summary: In Part I of this series of papers [Hiroshima Math. J. 43, No. 2, 239–264 (2013; Zbl 1296.57011)], we made Riley’s definition of Heckoid groups for 2-bridge links explicit, and gave a systematic construction of epimorphisms from 2-bridge link groups onto Heckoid groups, generalizing Riley’s construction. In this paper, we give a complete characterization of upper-meridian-pair-preserving epimorphisms from 2-bridge link groups onto even Heckoid groups, by proving that they are exactly the epimorphisms obtained by the systematic construction.

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57M50 General geometric structures on low-dimensional manifolds 20F06 Cancellation theory of groups; application of van Kampen diagrams
##### Keywords:
Heckoid groups; small cancellation theory
Full Text:
##### References:
 [1] E. Hecke, Über die Bestimung Dirichletscher Reihen durch ihre Funktionalgleichung , Math. Ann. 112 (1936), 664-699. · Zbl 0014.01601 [2] D. Lee and M. Sakuma, Simple loops on $$2$$-bridge spheres in $$2$$-bridge link complements , Electron. Res. Announc. Math. Sci. 18 (2011), 97-111. · Zbl 1225.57009 [3] D. Lee and M. Sakuma, Epimorphisms between $$2$$-bridge link groups: homotopically trivial simple loops on $$2$$-bridge spheres , Proc. London Math. Soc. 104 (2012), 359-386. · Zbl 1250.57015 [4] D. Lee and M. Sakuma, Homotopically equivalent simple loops on $$2$$-bridge spheres in $$2$$-bridge link complements (I) , arXiv: · Zbl 1225.57009 [5] D. Lee and M. Sakuma, Homotopically equivalent simple loops on $$2$$-bridge spheres in $$2$$-bridge link complements (II) , arXiv: · Zbl 1225.57009 [6] D. Lee and M. Sakuma, Homotopically equivalent simple loops on $$2$$-bridge spheres in $$2$$-bridge link complements (III) , arXiv: · Zbl 1225.57009 [7] D. Lee and M. Sakuma, A variation of McShane’s identity for $$2$$-bridge links , arXiv: · Zbl 1311.57022 [8] D. Lee and M. Sakuma, Epimorphisms from 2-bridge link groups onto Heckoid groups (I) , to appear in Hiroshima Math. J.. · Zbl 1296.57011 [9] D. Lee and M. Sakuma, Homotopically equivalent simple loops on $$2$$-bridge spheres in Heckoid orbifold for $$2$$-bridge links , preliminary notes. · Zbl 1255.57006 [10] R. C. Lyndon and P. E. Schupp, Combinatorial group theory , Springer-Verlag, Berlin, 1977. · Zbl 0368.20023 [11] B. B. Newman, Some results on one-relator groups , Bull. Amer. Math. Soc. 74 (1968), 568-571. · Zbl 0174.04603 [12] R. Riley, Algebra for Heckoid groups , Trans. Amer. Math. Soc. 334 (1992), 389-409. · Zbl 0786.57004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.