On infinite classes of genus two 1-bridge knots
Commun. Korean Math. Soc. 2004 Vol. 19, No. 3, 531-544
Printed September 1, 2004
Soo Hwan Kim, Yangkok Kim
Dongeui University, Dongeui University
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
MSC numbers : Primary 57M12, 57M25; Secondary 57M50, 57N10
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