# ON THE CRYSTALLIZATION OF 3-MANIFOLDS ASSOCIATED WITH POLYHEDRAL SCHEMATA

• Ko, Kyung-Hee ;
• Song, Hyun-Jong
• Published : 1999.03.01
• 31 4

#### Abstract

In this paper we introduce a method of presenting 3-manifolds by polyhedral schemata with 2 vertices so that they may be naturally associated with given crystallizations of 3-manifolds. As applications, we explicitly present crystallizations of n-fold cyclic branched coverings of S over 2-bridge knots.

#### Keywords

crystallizations;polyhedral schemata;Heegaard diagrams;cyclic branched coverings;2-bridge knots

#### References

1. Proc. Amer Math. Soc. v.73 Crystallizations of 2-fold branched converings of $S^3$ M. Ferri
2. Annals of Math. Studies #56 Knot groups L. P. Neuwirth
3. Proc. Amer Math. Soc. v.81 Exterding the concept of genus to dimension n C. Gagliardi
4. Knots and links D. Rolfsen
5. Amer. Math. Soc. v.35 The branched coverings of 2-bridge knots and links J. Minkus
6. Clissical Tessellations and Three-Manifolds J. S. Montesinos
7. Discrete Math. v.57 Graph-encoded 3-manifolds A. Mandel;S. Lins
8. Trans. Amer. Math. Soc. v.213 Heegaard splittings of branched coverings of $S^3$ J. S. Birman;H. M. Hilden
9. Pro. Camb. Phil. Soc. v.64 An algorithm for the construction of 3-manifolds from 2-complexes L. P. Neuwirth
10. Boll. Un. Mat. Ital. v.12 Diagrammi di Heegaard e triangolazione contratta M. Pezzana
11. Knots G. Burde;H. Zieschang