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Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 32-554
Full Name: Soo hwan Kim
Position: Professor
Age: ON
Sex: Male
Address: Department of mathematics, Dongeui University, Busan
Country: KOREA
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E-mail address: sootopology@hanmail.net
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Title of the Paper: On the 2-bridge knots of Dunwoody (1,1)-knots
Authors as they appear in the Paper: Soo hwan Kim and Yangkok Kim
Email addresses of all the authors: sootopology@hanmail.net, ykkim@deu.ac.kr
Number of paper pages: 13
Abstract: Every $(1,1)$-knot is represented by a 4-tuple of integers $(a,b,c,r),$ where $a>0,$ $b\geq 0,$ $c\geq 0,$ $d=2a+b+c,r\in \mathbb{Z}_{d},$ and it is well known that all $2$-bridge knots and torus knots are $(1,1)$-knots. In this paper, we describe some conditions for 4-tuples which determine $2$-bridge knots and determine all $4$-tuples representing any given $2$-bridge knot.
Keywords: Dunwoody manifold, Heegaard splitting, Heegaard diagram, (1,1)-decomposition, Cyclic branched covering, Crystallization
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