[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2004.19.3.531

ON INFINITE CLASSES OF GENUS TWO 1-BRIDGE KNOTS

Kim, Soo-Hwan (Department of Mathematics Dongeui University)
Kim, Yang-Kok (Department of Mathematics Dongeui University)

Publication Information

Communications of the Korean Mathematical Society / v.19, no.3, 2004 , pp. 531-544 More about this Journal

Abstract

We study a family of 2-bridge knots with 2-tangles in the 3-sphere admitting a genus two 1-bridge splitting. We also observe a geometric relation between (g - 1, 1)-splitting and (g,0)- splitting for g = 2,3. Moreover we construct a family of closed orientable 3-manifolds which are n-fold cyclic coverings of the 3-sphere branched over those 2-bridge knots.

Keywords

Heegaard Diagram; (2,1)-decomposition; covering space;

Citations & Related Records

Reference

1	Surgery on knots in solid tori / [ D. Gabai ] / Topology DOI ScienceOn
2	The knots in D<TEX>$^2 {\times} S^1$</TEX> with non-trivial Dehn surgery yielding D<TEX>$^2 {\times} D^1$</TEX> / [ J. Berge ] / Topology Appl. DOI ScienceOn
3	1-bridge braids in solid tori / [ D. Gabai ] / Topology Appl. DOI ScienceOn
4	Genus two Heegaard splittings of exteriors of knots and the disjoint curve property / [ H. Goda;C. Hayashi;N. Yoshida ] / Kobe J. Math.
5	The arithmeticity of the figure eight knot orbifolds / [ H. M. Hilden;M. T. Lozano;J. M. Montesinos-Amilibia;Apanasov, W. D. Neumann(ed.);A. W. Reid(ed.);L. Siebenmann(ed.);Walter de Gruyter(ed.) ] / Topology
6	Classification of unknotting tunnels for two bridge knots / [ T. Kobayashi ] / Geom. Topol. Monogr.
7	Heegaard splittings of exteriors of two bridge knots / [ T. Kobayashi ] / Geom. Topol. DOI
8	Incompressibility of surfaces in surgered 3-manifold / [ Y-Q. Wu ] / Topology
9	<TEX>${\partial}$</TEX>-reducing Dehn surgeries and 1-bridge knots / [ Y-Q. Wu ] / Math. Ann.
10	Incompressible surfaces and Dehn surgery on 1-bridge knots in handlebodies / [ Y-Q. Wu ] / Math. Proc. Cambridge Philos. Soc. DOI ScienceOn